Patent Publication Number: US-5426651-A

Title: Method for the automatic generation of test sequences

Description:
BACKGROUND OF THE INVENTION 
     The invention relates to a method for the automatic generation, from a system or protocol specified as an FSM, of sequences of input signals, which are to be supplied to a system to be tested, together with the associated output signals which are to be received from the system to be tested and which serve to establish whether or not the implementation is in a particular state. 
     A useful introduction to the problems addressed by the present invention is provided in the U.S. Pat. No. 4,692,921 of AT&amp;T, where it is stated that there has always been a need for the functioning of electronic systems to be tested and verified against the intended functioning. In the past, tests intended for this purpose were devised by the system designers who, in doing so, depended on their knowledge of the system design and the likely behaviour thereof. As VLSI (Very Large Scale Integration) progressed, this became more difficult. One of the causes is that there are no internal test points which can be approached to isolate faults. Another reason is that, in general, there are no repair possibilities. A further reason is that the design philosophy has changed from designs which attempt to limit the number of transistors to designs which intend to reduce the &#34;real estate&#34; and the input/output complexity. 
     The number of active elements in an integrated circuit (IC) amounts to hundreds of thousands, and is still increasing. The masks with which these ICs are produced are very expensive and it is therefore extremely important that the ICs fabricated therewith function according to their specifications. Another point is that during fabrication no defects must be introduced, such as active elements which stick on the value 1 or 0. Even more importantly, it must be possible for ICs containing such defects to be detected quickly and simply. 
     Hereinbelow, as in the said U.S. Patent, use will be made of the possibility to describe digital systems as &#34;finite state machines&#34; (FSM) which, in response to certain sequences of input signals, emit certain sequences of output signals. These are called finite state machines because, in contrast to analog systems, they can adopt only a limited number of internal states and jump from one state to another state (&#34;state transition&#34; or &#34;edge&#34;) in response to one or more input signals. An FSM can therefore also be regarded as having been specified by its reaction to input signals (in the form of output signals). An FSM can be represented both in the form of a diagram and in the form of tables. 
     Said U.S. Patent discloses a method for developing test sequences for evaluating the design or the functioning of a digital system presented as an FSM. According to the method disclosed, the entire FSM is run through, and all the state transitions are tested. For each state transition, a test is developed which comprises a three-part test sequence. The first part is a sequence which puts the FSM into a first state. The second part, by supplying an input signal, causes a state transition from the first state to a second state. The third part is formed by a sequence which is unique for the second state and whose purpose is to check whether the implemented FSM has indeed reached the state desired (in accordance with the specified FSM). This part is therefore formed by a sequence of input signals together with the associated output signals, which is unique with respect to all the other states of the FSM and can serve as a &#34;signature&#34;, as it were, for that state. The invention is in the field of the automatic generation, from a system or protocol specified as an FSM, of sequences of input signals, which are to be supplied to a system to be tested, together with the associated output signals which are to be received from the system to be tested and which serve to establish whether or not the implementation is in a particular state, in other words the generation of unique input/output sequences (UIO sequences), and is comparable to process step 1 in the said patent. 
     According to the known method for generating this type of sequences, the UIO sequences are generated via three intermediate steps. In the first intermediate step, a table is generated containing the &#34;labels&#34; of all state transitions and a designation of the &#34;head&#34; and the &#34;tail&#34; state(s) of each of those labels. In the second intermediate step, all the state transitions having a &#34;null&#34; input are identified, as well as all the state transitions whose tail state is identical to a head state of a state transition having a null input. Consecutive state transitions of this type then form a &#34;meta&#34; state transition. The meta state transitions and the remaining (non-null input) state transitions are incorporated in a second table. As a third step, this table is sorted according to state transition labels, and the labels which occur only once are marked. The labels are then sorted according to head state. The marked labels are unique. Finally, in a fourth step, the third step is repeated a number of times, resulting, generally, in a unique UIO sequence. 
     Generating UIO sequences in this manner have a number of drawbacks. Notably, the known method results in only one UIO sequence for a particular state. Furthermore, when carrying out the said fourth step of the known method, there is the risk that this ends up in an &#34;infinite loop&#34;, namely if no UIO sequence can be found. 
     The method according to the present invention, in contrast, generates all the UIO sequences which are possible for a particular state (from which, incidentally, the shortest is preferably selected). 
     SUMMARY OF THE INVENTION 
     The invention therefore relates to a method for the automatic generation, from a system or protocol specified as an FSM, of sequences of input signals, which are to be supplied to a system to be tested, together with the associated output signals which are to be received from the system to be tested and which serve to establish whether or not the implementation is in a particular state. The invention is characterised by a first step in which the FSM is converted into a first table containing input-output signals and associated start and end states; 
     a second step in which, for a particular state, a second table is generated by copying the first table and, in doing so, marking that state as a start state and all the other states as a valid end state; 
     a third step in which for each of the other states a third table is generated by copying the first or the second table, adding thereto at least one escape state and, in those third tables, in each case marking that other state as a start state and that escape state as a valid end state for all invalid input-output signals; 
     a fourth step in which a fourth table is generated by logically combining the second table with all the third tables to give combination states which occur both in the second and in all the third tables, that combination state being marked as a start state which is marked as a start state in both the second and in all the third tables, and all those combination states being marked as an end state which are marked as an end state in both the second and in all the third tables; 
     a fifth step in which each sequence of input-output signals from the fourth table, starting from a combination state marked as a start state and ending in a combination state marked as an end state, is selected as one of the desired test sequences and is stored in a fifth table. 
     To put it more simply, the method according to the invention successively comprises a conversion of the FSM--stored, for example, in a computer file--into a &#34;base table&#34; from which, for example for each state, two types of tables are generated. First--for that state--a table is produced in which, starting from that state as a start state, all the (according to the FSM) legal end states which are possible from that start state are indicated; this table could be called &#34;possibilities table&#34;. This table thus comprises all the legal IO sequences which are possible from that start state. Thereafter--or at the same time--a table is produced for all the other states, in which table, starting from that &#34;other&#34; state as a start state, all nonlegal IO sequences are registered. A &#34;virtual&#34; end state for those nonlegal IO sequences is introduced in the form of an &#34;escape state&#34;. In other words, if a nonlegal IO sequence is supplied in a particular state, the system always ends up in such an escape state. Thus one table has now been generated for the initial state, comprising legal IO sequences from that state, the &#34;possibilities table&#34; and a series of tables--&#34;impossibilities tables&#34;--comprising all nonlegal IO sequences from the other states. In order to establish that a system at a given time is in a particular state, it is sufficient to establish that an IO sequence from that state is legal, whereas that IO sequence from all the other states is nonlegal and results in an escape state. In that case, therefore, a UIO sequence is involved. All the UIO sequences for a particular state can thus be found by, starting from that state, logically combining its &#34;possibilities table&#34; with the &#34;impossibilities tables&#34; of all the other states; these sequences therefore must occur in the &#34;possibilities table&#34; AND in all those &#34;impossibilities tables&#34;. The IO sequences satisfying this condition are UIO sequences for that state to be tested. 
     The above method can be carried out for only one state, for example the start state of the FSM, or--successively or simultaneously--for more or even all the states. The method can then preferably be carried out simultaneously for all states, in which case in the second step a second table is generated for all states by copying the first table and, in doing so, marking those various states as a start state in the various second tables, and all the other states as a valid end state; 
     in the third step a third table is generated for all the states by copying the first or the second table, adding thereto at least one escape state and in each case marking those various states as a start state in those various third tables and that escape state as a valid end state for all invalid input-output signals; 
     a fourth step in which a fourth table is generated by logically combining the second tables with the third tables as indicated, resulting in combination states which occur both in the second and in all the third tables, those combination states being marked as a start state which are marked as a start state in both the second and in the third tables, and all those combination states being marked as an end state which are marked as an end state in both the second and in the third tables; 
     a fifth step in which the sequences of input-output signals which start with a combination state marked as a start state and end in a combination state marked as an end state are selected as a desired test sequence and are stored in the fifth table. 
     By calculating the UIO sequences for all the states simultaneously, the method can thus work very efficiently. To put it simply, in doing so, a &#34;possibilities table&#34; is generated for all states as well as an &#34;impossibilities table&#34; for all states. Subsequently, for each state, the &#34;possibilities table&#34; of that state is logically combined with the &#34;impossibilities tables&#34; of the remaining states, resulting in UIO sequences for each state, by means of which those states can therefore be identified. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 depicts a state diagram of a finite state machine. 
     FIG. 2 depicts another state diagram of a finite state machine. 
     FIG. 3 presents a flow chart describing the method of the invention for developing test sequences. 
    
    
     ILLUSTRATIVE EMBODIMENTS 
     An example will be given below of the generation of the UIO sequences for state 0 in the FSM of FIG. 1, the same FSM as is shown in U.S. Pat. No. 4,692,921. In doing so, the steps will be followed which are specified in the main claim. These steps are illustrated in FIG. 3. 
     I. In the first step 101, the FSM is converted into a first table containing input-output signals and start and end states associated therewith; see TABLE 1. 
     II. In the second step 102, a second table is generated for a particular initial state--in this case state 0--by copying the first table and, in doing so, marking that state as a start state, and all the other states as valid end states; see TABLE 2. 
     III. In the third step 103, a third table is generated for each state other than the initial state by copying the first or the second table, adding thereto an escape state, and in each case marking, in those third tables, that other state as a start state and that escape state as a valid end state for all invalid inputoutput signals (hereinafter, a,b,c, . . . indicate the various escape states); see TABLE 3. 
     IV. In the fourth step 104, a fourth table is generated by logically combining (` `) the second table (the &#34;possibilities table&#34;) see TABLE 2, with all the third tables (the &#34;impossibilities tables&#34;) see TABLE 3 to give combination states which occur both in the second and in all the third tables, that combination state being marked as a start state which is marked in both the third table and in all the third tables as a start state, and all those combination states being marked as an end state which are marked as an end state both in the second table and in all the third tables. 
     First of all, the generation of the logical combination (` `) of all &#34;impossibilities tables&#34; of the states≠state 0 is demonstrated; see TABLE 4. 
     Then the &#34;possibilities table&#34; of state 0 is logically combined with the &#34;impossibilities tables&#34; of the states≠0; see TABLE 5. 
     V. In the fifth step 105, the sequences of input-output signals which start with a combination state marked as a start state (`S`) and which end in a combination state marked as an end state (`E`) are selected as one of the desired test sequences and are stored in a fifth table. 
     This works as follows (see TABLE 5): 
     Starting from the start state, it is ascertained which &#34;paths&#34; lead to an end state. The following sequences are produced: ##STR1## 
     The UIO sequences are therefore 
     
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A/N → D/X                                                          
A/N → D/X → N/Y                                             
A/N → D/X → N/Y → R/N                                
A/N → D/X → N/Y → R/N → A/N                   
Etcetera                                                                  
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     As all the sequences start with the same sequence A/N→D/X, the remaining sequences in fact do not add anything. The only relevant UIO sequence is therefore the UIO sequence A/N→D/X, which is suitable as a &#34;signature&#34; for state 0. 
     In the same way, UIO sequences can be generated for the other FSM states, such as for state 7; see TABLE 6. 
     Two (independent) IO sequences are produced from this system, which can both be used as a UIO sequence, viz. 
     D/N (which effects the transition from state (1) to (2)); 
     B/N→N/Z (which successively effects the transition from state (3) to (4) and then from (4) to (5)). 
     Finally, the elaboration is also given for an FSM which is shown in FIG. 2 and which is taken from U.S. Pat. No. 4,991,176 (AT&amp;T), specifically for the state of that FSM 1; see TABLE 7. The result was obtained in the same manner as described hereinabove, in this case even as many as five UIO sequences: 
     (A/X A/X) 
     (A/X C/Y A/X) 
     (A/X C/Y B/Z) 
     (C/Y A/X) 
     (C/Y B/Z) 
     According to Dijkstra&#39;s known shortest-path method, it can be calculated that (A/X A/X) is the shortest of these UIO sequences. 
     For the sake of completeness, TABLE 8 shows the source code of the computer program with which the method according to the invention can be carried out, which program was also used to produce the above illustrative examples. 
     REFERENCES 
     U.S. Pat. No. 4,692,921 (AT&amp;T) 
     
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The following applies in the tables below:                                
Start state: S                                                            
End state: E                                                              
`Possibilities table` for the state n: M[n]                               
`Impossibilities tabel` for the state m: compl(M[m])                      
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                       TABLE 1                                                     
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A/N     R/N     D/X    N/Y   B/N  C/N   N/Z  D/N                          
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0SE  1      0       --   --    --   --    --   --                         
1E   --     0       2    --    --   --    --   --                         
2E   --     0       --   3     --   --    --   --                         
3E   --     0       --   --    1    4     --   --                         
4E   5      0       --   --    --   --    --   --                         
5E   --     0       --   --    --   --    6    --                         
6E   --     0       --   7     --   --    --   --                         
7E   --     0       --   --    5    --    --   0                          
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                       TABLE 2                                                     
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M[0]                                                                      
A/N     R/N     D/X    N/Y   B/N  C/N   N/Z  D/N                          
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0SE  1      0       --   --    --   --    --   --                         
1E   --     0       2    --    --   --    --   --                         
2E   --     0       --   3     --   --    --   --                         
3E   --     0       --   --    1    4     --   --                         
4E   5      0       --   --    --   --    --   --                         
5E   --     0       --   --    --   --    6    --                         
6E   --     0       --   7     --   --    --   --                         
7E   --     0       --   --    5    --    --   0                          
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                       TABLE 3                                                     
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A/N     R/N     D/X    N/Y   B/N  C/N   N/Z  D/N                          
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compl(M[1])                                                               
aE   a      a       a    a     a    a     a    a                          
0    1      0       a    a     a    a     a    a                          
1S   a      0       2    a     a    a     a    a                          
2    a      0       a    3     a    a     a    a                          
3    a      0       a    a     1    4     a    a                          
4    5      0       a    a     a    a     a    a                          
5    a      0       a    a     a    a     6    a                          
6    a      0       a    7     a    a     a    a                          
7    a      0       a    a     5    a     a    0                          
compl(M[2])                                                               
bE   b      b       b    b     b    b     b    b                          
0    1      0       b    b     b    b     b    b                          
1    b      0       2    b     b    b     b    b                          
2S   b      0       b    3     b    b     b    b                          
3    b      0       b    b     1    4     b    b                          
4    5      0       b    b     b    b     b    b                          
5    b      0       b    b     b    b     6    b                          
6    b      0       b    7     b    b     b    b                          
7    b      0       b    b     5    b     b    0                          
compl(M[3])                                                               
cE   c      c       c    c     c    c     c    c                          
0    1      0       c    c     c    c     c    c                          
1    c      0       2    c     c    c     c    c                          
2    c      0       c    3     c    c     c    c                          
3S   c      0       c    c     1    4     c    c                          
4    5      0       c    c     c    c     c    c                          
5    c      0       c    c     c    c     6    c                          
6    c      0       c    7     c    c     c    c                          
7    c      0       c    c     5    c     c    0                          
compl(M[4])                                                               
dE   d      d       d    d     d    d     d    d                          
0    1      0       d    d     d    d     d    d                          
1    d      0       2    d     d    d     d    d                          
2    d      0       d    3     d    d     d    d                          
3    d      0       d    d     1    4     d    d                          
4S   5      0       d    d     d    d     d    d                          
5    d      0       d    d     d    d     6    d                          
6    d      0       d    7     d    d     d    d                          
7    d      0       d    d     5    d     d    0                          
compl(M[5])                                                               
eE   e      e       e    e     e    e     e    e                          
0    1      0       e    e     e    e     e    e                          
1    e      0       2    e     e    e     e    e                          
2    e      0       e    3     e    e     e    e                          
3    e      0       e    e     1    4     e    e                          
4    5      0       e    e     e    e     e    e                          
5S   e      0       e    e     e    e     6    e                          
6    e      0       e    7     e    e     e    e                          
7    e      0       e    e     5    e     e    0                          
compl(M[6])                                                               
fE   f      f       f    f     f    f     f    f                          
0    1      0       f    f     f    f     f    f                          
1    f      0       2    f     f    f     f    f                          
2    f      0       f    3     f    f     f    f                          
3    f      0       f    f     1    4     f    f                          
4    5      0       f    f     f    f     f    f                          
5    f      0       f    f     f    f     6    f                          
6S   f      0       f    7     f    f     f    f                          
7    f      0       f    f     5    f     f    0                          
compl(M[7])                                                               
gE   9      9       9    9     9    9     9    9                          
0    1      0       g    g     g    g     g    g                          
1    g      0       2    g     g    g     g    g                          
2    g      0       g    3     g    g     g    g                          
3    g      0       g    9     1    4     g    g                          
4    5      0       g    g     g    9     9    9                          
5    9      0       g    g     9    9     6    g                          
6    9      0       g    7     9    9     9    9                          
7S   9      0       g    g     5    g     g    0                          
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                                           TABLE 4                                 
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A/N       R/N  D/X  N/Y  B/N  C/N  N/Z  D/N                               
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compl(M[1]) compl(M[2])                                                   
12S  ab   00   2b   a3   ab   ab   ab   ab                                
abE  ab   ab   ab   ab   ab   ab   ab   ab                                
a3   ab   a0   ab   ab   a1   a4   ab   ab                                
2b   ab   0b   ab   3b   ab   ab   ab   ab                                
00   11   00   ab   ab   ab   ab   ab   ab                                
a4   a5   a0   ab   ab   ab   ab   ab   ab                                
a1   ab   a0   a2   ab   ab   ab   ab   ab                                
a0   a1   a0   ab   ab   ab   ab   ab   ab                                
3b   ab   0b   ab   ab   1b   4b   ab   ab                                
0b   1b   0b   ab   ab   ab   ab   ab   ab                                
11   ab   00   22   ab   ab   ab   ab   ab                                
a5   ab   a0   ab   ab   ab   ab   a6   ab                                
a2   ab   a0   ab   a3   ab   ab   ab   ab                                
1b   ab   0b   2b   ab   ab   ab   ab   ab                                
4b   5b   0b   ab   ab   ab   ab   ab   ab                                
22   ab   00   ab   33   ab   ab   ab   ab                                
a6   ab   a0   ab   a7   ab   ab   ab   ab                                
5b   ab   0b   ab   ab   ab   ab   6b   ab                                
33   ab   00   ab   ab   11   44   ab   ab                                
a7   ab   a0   ab   ab   a5   ab   ab   a0                                
6b   ab   0b   ab   7b   ab   ab   ab   ab                                
44   55   00   ab   ab   ab   ab   ab   ab                                
7b   ab   0b   ab   ab   5b   ab   ab   0b                                
55   ab   00   ab   ab   ab   ab   66   ab                                
66   ab   00   ab   77   ab   ab   ab   ab                                
77   ab   00   ab   ab   55   ab   ab   00                                
compl(M[1]) compl(M[2]) compl(M[3])                                       
123S abc  000  2bc  a3c  ab1  ab4  abc  abc                               
abcE abc  abc  abc  abc  abc  abc  abc  abc                               
ab4  ab5  ab0  abc  abc  abc  abc  abc  abc                               
ab1  abc  ab0  ab2  abc  abc  abc  abc  abc                               
a3c  abc  a0c  abc  abc  a1c  a4c  abc  abc                               
2bc  abc  0bc  abc  3bc  abc  abc  abc  abc                               
000  111  000  abc  abc  abc  abc  abc  abc                               
ab0  ab1  ab0  abc  abc  abc  abc  abc  abc                               
ab5  abc  ab0  abc  abc  abc  abc  ab6  abc                               
ab2  abc  ab0  abc  ab3  abc  abc  abc  abc                               
a4c  a5c  a0c  abc  abc  abc  abc  abc  abc                               
a1c  abc  a0c  a2c  abc  abc  abc  abc  abc                               
a0c  a1c  a0c  abc  abc  abc  abc  abc  abc                               
3bc  abc  0bc  abc  abc  1bc  4bc  abc  abc                               
0bc  1bc  0bc  abc  abc  abc  abc  abc  abc                               
111  abc  000  222  abc  abc  abc  abc  abc                               
ab6  abc  ab0  abc  ab7  abc  abc  abc  abc                               
ab3  abc  ab0  abc  abc  ab1  ab4  abc  abc                               
a5c  abc  a0c  abc  abc  abc  abc  a6c  abc                               
a2c  abc  a0c  abc  a3c  abc  abc  abc  abc                               
1bc  abc  0bc  2bc  abc  abc  abc  abc  abc                               
4bc  5bc  0bc  abc  abc  abc  abc  abc  abc                               
222  abc  000  abc  333  abc  abc  abc  abc                               
ab7  abc  ab0  abc  abc  ab5  abc  abc  ab0                               
a6c  abc  a0c  abc  a7c  abc  abc  abc  abc                               
5bc  abc  0bc  abc  abc  abc  abc  6bc  abc                               
333  abc  000  abc  abc  111  444  abc  abc                               
a7c  abc  a0c  abc  abc  a5c  abc  abc  a0c                               
6bc  abc  0bc  abc  7bc  abc  abc  abc  abc                               
444  555  000  abc  abc  abc  abc  abc  abc                               
7bc  abc  0bc  abc  abc  5bc  abc  abc  0bc                               
555  abc  000  abc  abc  abc  abc  666  abc                               
666  abc  000  abc  777  abc  abc  abc  abc                               
777  abc  000  abc  abc  555  abc  abc  000                               
compl(M[1]) compl(M[2]) compl(M[3]) compl(M[4])                           
1234S                                                                     
     abc5 0000 2bcd a3cd ab1d ab4d abcd abcd                              
abcdE                                                                     
     abcd abcd abcd abcd abcd abcd abcd abcd                              
ab4d ab5d ab0d abcd abcd abcd abcd abcd abcd                              
ab1d abcd ab0d ab2d abcd abcd abcd abcd abcd                              
a3cd abcd a0cd abcd abcd a1cd a4cd abcd abcd                              
abc5 abcd abc0 abcd abcd abcd abcd abc6 abcd                              
2bcd abcd 0bcd abcd 3bcd abcd abcd abcd abcd                              
0000 1111 0000 abcd abcd abcd abcd abcd abcd                              
ab0d ab1d ab0d abcd abcd abcd abcd abcd abcd                              
ab5d abcd ab0d abcd abcd abcd abcd ab6d abcd                              
ab2d abcd ab0d abcd ab3d abcd abcd abcd abcd                              
a4cd a5cd a0cd abcd abcd abcd abcd abcd abcd                              
a1cd abcd a0cd a2cd abcd abcd abcd abcd abcd                              
a0cd a1cd a0cd abcd abcd abcd abcd abcd abcd                              
abc6 abcd abc0 abcd abc7 abcd abcd abcd abcd                              
abc0 abc1 abc0 abcd abcd abcd abcd abcd abcd                              
3bcd abcd 0bcd abcd abcd 1bcd 4bcd abcd abcd                              
0bcd 1bcd 0bcd abcd abcd abcd abcd abcd abcd                              
1111 abcd 0000 2222 abcd abcd abcd abcd abcd                              
ab6d abcd ab0d abcd ab7d abcd abcd abcd abcd                              
ab3d abcd ab0d abcd abcd ab1d ab4d abcd abcd                              
a5cd abcd a0cd abcd abcd abcd abcd a6cd abcd                              
a2cd abcd a0cd abcd a3cd abcd abcd abcd abcd                              
abc7 abcd abc0 abcd abcd abc5 abcd abcd abc0                              
abc1 abcd abc0 abc2 abcd abcd abcd abcd abcd                              
1bcd abcd 0bcd 2bcd abcd abcd abcd abcd abcd                              
4bcd 5bcd 0bcd abcd abcd abcd abcd abcd abcd                              
2222 abcd 0000 abcd 3333 abcd abcd abcd abcd                              
ab7d abcd ab0d abcd abcd ab5d abcd abcd ab0d                              
a6cd abcd a0cd abcd a7cd abcd abcd abcd abcd                              
abc2 abcd abc0 abcd abc3 abcd abcd abcd abcd                              
5bcd abcd 0bcd abcd abcd abcd abcd 6bcd abcd                              
3333 abcd 0000 abcd abcd 1111 4444 abcd abcd                              
a7cd abcd a0cd abcd abcd a5cd abcd abcd a0cd                              
abc3 abcd abc0 abcd abcd abc1 abc4 abcd abcd                              
6bcd abcd 0bcd abcd 7bcd abcd abcd abcd abcd                              
4444 5555 0000 abcd abcd abcd abcd abcd abcd                              
abc4 abc5 abc0 abcd abcd abcd abcd abcd abcd                              
7bcd abcd 0bcd abcd abcd 5bcd abcd abcd 0bcd                              
5555 abcd 0000 abcd abcd abcd abcd 6666 abcd                              
6666 abcd 0000 abcd 7777 abcd abcd abcd abcd                              
7777 abcd 0000 abcd abcd 5555 abcd abcd 0000                              
 compl(M[1]) compl(M[2]) compl(M[3]) compl(M[4]) compl(M[5])              
12345S                                                                    
     abc5e                                                                
          00000                                                           
               2bcde                                                      
                    a3ede                                                 
                         ab1de                                            
                              ab4de                                       
                                   abcd6                                  
                                        abcde                             
abcdeE                                                                    
     abcde                                                                
          abcde                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abede                                  
                                        abcde                             
abcd6                                                                     
     abcde                                                                
          abcd0                                                           
               abcde                                                      
                    abcd7                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
ab4de                                                                     
     ab5de                                                                
          ab0de                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
ab1de                                                                     
     abcde                                                                
          ab0de                                                           
               ab2de                                                      
                    abcde                                                 
                         abed,                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
a3cde                                                                     
     abcde                                                                
          a0cde                                                           
               abcde                                                      
                    abcde                                                 
                         a1cde                                            
                              a4ede                                       
                                   abcde                                  
                                        abcde                             
abc5e                                                                     
     abcde                                                                
          abc0e                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abc6e                                  
                                        abcde                             
2bcde                                                                     
     abcde                                                                
          0bcde                                                           
               abcde                                                      
                    3bcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
00000                                                                     
     11111                                                                
          00000                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
abcd7                                                                     
     abcde                                                                
          abcd0                                                           
               abcde                                                      
                    abcde                                                 
                         abcd5                                            
                              abcde                                       
                                   abcde                                  
                                        abcd0                             
abcd0                                                                     
     abcd1                                                                
          abcd0                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abede                                  
                                        abcde                             
ab0de                                                                     
     ab1de                                                                
          ab0de                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
ab5de                                                                     
     abcde                                                                
          ab0de                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   ab0de                                  
                                        abcde                             
ab2de                                                                     
     abcde                                                                
          ab0de                                                           
               abcde                                                      
                    ab3de                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
a4cde                                                                     
     a5cde                                                                
          a0cde                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abede                                       
                                   abcde                                  
                                        abcde                             
a1cde                                                                     
     abede                                                                
          a0cde                                                           
               a2cde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
a0cde                                                                     
     a1cde                                                                
          a0cde                                                           
               abcde                                                      
                    abcde                                                 
                         abcd0                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
abc6e                                                                     
     abcde                                                                
          abc0e                                                           
               abcde                                                      
                    abc7e                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
abc0e                                                                     
     abc1e                                                                
          abc0e                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
3bcde                                                                     
     abcde                                                                
          0bcde                                                           
               abcde                                                      
                    abcde                                                 
                         1bcde                                            
                              4bcde                                       
                                   abcde                                  
                                        abcde                             
0bcde                                                                     
     1bcde                                                                
          0bcde                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
11111                                                                     
     abcde                                                                
          00000                                                           
               22222                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
abcd5                                                                     
     abcde                                                                
          abcd0                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcd6                                  
                                        abcde                             
abcd1                                                                     
     abcde                                                                
          abcd0                                                           
               abcd2                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
ab0de                                                                     
     abcde                                                                
          ab0de                                                           
               abcde                                                      
                    ab7de                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
ab3de                                                                     
     abcde                                                                
          ab0de                                                           
               abcde                                                      
                    abcde                                                 
                         ab1de                                            
                              ab4de                                       
                                   abcde                                  
                                        abcde                             
a5cde                                                                     
     abcde                                                                
          a0cde                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   a6cde                                  
                                        abcde                             
a2cde                                                                     
     abcde                                                                
          a0cde                                                           
               abcde                                                      
                    a3cde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
abc7e                                                                     
     abcde                                                                
          abc0e                                                           
               abcde                                                      
                    abcde                                                 
                         abc5e                                            
                              abcde                                       
                                   abede                                  
                                        abc0e                             
abc1e                                                                     
     abcde                                                                
          abc0e                                                           
               abc2e                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
1bcde                                                                     
     abcde                                                                
          0bcde                                                           
               2bcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
4bcde                                                                     
     5bcde                                                                
          0bcde                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
22222                                                                     
     abcde                                                                
          00000                                                           
               abcde                                                      
                    33333                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
abcd2                                                                     
     abcde                                                                
          abcd0                                                           
               abcde                                                      
                    abcd3                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
ab7de                                                                     
     abcde                                                                
          ab0de                                                           
               abcde                                                      
                    abcde                                                 
                         ab5de                                            
                              abcde                                       
                                   abcde                                  
                                        ab0de                             
a6cde                                                                     
     abcde                                                                
          a0cde                                                           
               abcde                                                      
                    a7cde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
abc2e                                                                     
     abcde                                                                
          abe0e                                                           
               abcde                                                      
                    abc3e                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
5bcde                                                                     
     abcde                                                                
          0bcde                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   6bcde                                  
                                        abcde                             
33333                                                                     
     abcde                                                                
          00000                                                           
               abcde                                                      
                    abcde                                                 
                         11111                                            
                              44444                                       
                                   abcde                                  
                                        abcde                             
abcd3                                                                     
     abcde                                                                
          abcd0                                                           
               abcde                                                      
                    abcde                                                 
                         abcd1                                            
                              abcd4                                       
                                   abede                                  
                                        abcde                             
a7cde                                                                     
     abcde                                                                
          a0,de                                                           
               abcde                                                      
                    abcd,                                                 
                         a5cde                                            
                              abcde                                       
                                   abcde                                  
                                        a0cde                             
abc3e                                                                     
     abcde                                                                
          abc0e                                                           
               abcde                                                      
                    abcde                                                 
                         abc1e                                            
                              abc4e                                       
                                   abcde                                  
                                        abcde                             
6bcde                                                                     
     abcde                                                                
          0bcde                                                           
               abcde                                                      
                    7bcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
44444                                                                     
     55555                                                                
          00000                                                           
               abcde                                                      
                    abcde                                                 
                         abede                                            
                              abcde                                       
                                   abede                                  
                                        abcde                             
abcd4                                                                     
     abcd5                                                                
          abcd0                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
abc4e                                                                     
     abc5e                                                                
          abe0e                                                           
               abcde                                                      
                    abcde                                                 
                         abede                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
7bcde                                                                     
     abcde                                                                
          0bcde                                                           
               abcde                                                      
                    abcde                                                 
                         5bcde                                            
                              abcde                                       
                                   abcde                                  
                                        0bcde                             
55555                                                                     
     abcde                                                                
          00000                                                           
               abcde                                                      
                    abcde                                                 
                         abcde                                            
                              abcde                                       
                                   66666                                  
                                        abcde                             
66666                                                                     
     abcde                                                                
          00000                                                           
               abcde                                                      
                    77777                                                 
                         abcde                                            
                              abcde                                       
                                   abcde                                  
                                        abcde                             
77777                                                                     
     abede                                                                
          00000                                                           
               abcde                                                      
                    abcde                                                 
                         55555                                            
                              abcde                                       
                                   abcde                                  
                                        00000                             
compl(M[1]) compl(M[2]) compl(M[3]) compl(M[4]) compl(M[5]) compl(M[6])   
123456S                                                                   
     abc5ef                                                               
          000000                                                          
               2bcdef                                                     
                    a3cde7                                                
                         ab1def                                           
                              ab4def                                      
                                   abcd6f                                 
                                        abcdef                            
abcdefE                                                                   
     abcdef                                                               
          abcdef                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
abcd6f                                                                    
     abcdef                                                               
          abcd0f                                                          
               abcdef                                                     
                    abcd7f                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
ab4def                                                                    
     ab5def                                                               
          ab0def                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
ab1def                                                                    
     abcdef                                                               
          ab0def                                                          
               ab2def                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
a3cde7                                                                    
     abcdef                                                               
          a0cde0                                                          
               abcdef                                                     
                    abcdef                                                
                         a1cde5                                           
                              a4cdef                                      
                                   abcdef                                 
                                        abcde0                            
abc5ef                                                                    
     abcdef                                                               
          abc0ef                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abc6ef                                 
                                        abcdef                            
2bcdef                                                                    
     abcdef                                                               
          0bcdef                                                          
               abedef                                                     
                    3bcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
000000                                                                    
     111111                                                               
          000000                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
abcd7f                                                                    
     abcdef                                                               
          abcd0f                                                          
               abcdef                                                     
                    abcdef                                                
                         abcd5f                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcd0f                            
abcd0f                                                                    
     abcd1f                                                               
          abcd0f                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
ab0def                                                                    
     ab1def                                                               
          ab0def                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
ab5def                                                                    
     abcdef                                                               
          ab0def                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   ab6def                                 
                                        abcdef                            
ab2def                                                                    
     abcdef                                                               
          ab0def                                                          
               abcdef                                                     
                    ab3def                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
abcde0                                                                    
     abcde1                                                               
          abcde0                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
a4cdef                                                                    
     a5cdef                                                               
          a0cdef                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
a1cde5                                                                    
     abcdef                                                               
          a0cde0                                                          
               a2cdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcde6                                 
                                        abcdef                            
a0cde0                                                                    
     a1cde1                                                               
          a0cde0                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
abc6ef                                                                    
     abcdef                                                               
          abc0ef                                                          
               abcdef                                                     
                    abc7ef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
abc0ef                                                                    
     abc1ef                                                               
          abc0ef                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
3bcdef                                                                    
     abcdef                                                               
          0bcdef                                                          
               abcdef                                                     
                    abcdef                                                
                         1bcdef                                           
                              4bcdef                                      
                                   abcdef                                 
                                        abcdef                            
0bcdef                                                                    
     1bcdef                                                               
          0bcdef                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
111111                                                                    
     abcdef                                                               
          000000                                                          
               222222                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
abcd5f                                                                    
     abcdef                                                               
          abcd0f                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcd6f                                 
                                        abcdef                            
abcd1f                                                                    
     abcdef                                                               
          abcd0f                                                          
               abcd2f                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
ab6def                                                                    
     abcdef                                                               
          ab0def                                                          
               abcdef                                                     
                    ab7def                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
ab3def                                                                    
     abcdef                                                               
          ab0def                                                          
               abcdef                                                     
                    abcdef                                                
                         ab1def                                           
                              ab4def                                      
                                   abcdef                                 
                                        abcdef                            
abcde1                                                                    
     abcdef                                                               
          abcde0                                                          
               abcde2                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abedef                            
a0cdef                                                                    
     a1cdef                                                               
          a0cdef                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
a5cdef                                                                    
     abcdef                                                               
          a0cdef                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   a6cdef                                 
                                        abcdef                            
abcde6                                                                    
     abcdef                                                               
          abcde0                                                          
               abcdef                                                     
                    abcde7                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
a2cdef                                                                    
     abcdef                                                               
          a0cdef                                                          
               abcdef                                                     
                    a3cdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
a1cde1                                                                    
     abcdef                                                               
          a0cde0                                                          
               a2cde2                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
abc7ef                                                                    
     abcdef                                                               
          abc0ef                                                          
               abcdef                                                     
                    abedef                                                
                         abc5ef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abc0ef                            
abc1ef                                                                    
     abcdef                                                               
          abc0ef                                                          
               abc2ef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
1bcdef                                                                    
     abcdef                                                               
          0bcdef                                                          
               2bcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
4bcdef                                                                    
     5bcdef                                                               
          0bcdef                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
222222                                                                    
     abcdef                                                               
          000000                                                          
               abcdef                                                     
                    333333                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
abcd2f                                                                    
     abcdef                                                               
          abcd0f                                                          
               abcdef                                                     
                    abcd3f                                                
                         abedef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
ab7def                                                                    
     abcdef                                                               
          ab0def                                                          
               abcdef                                                     
                    abcdef                                                
                         ab5def                                           
                              abcdef                                      
                                   abcdef                                 
                                        ab0def                            
abcde2                                                                    
     abcdef                                                               
          abcde0                                                          
               abcdef                                                     
                    abcde3                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
a1cdef                                                                    
     abcdef                                                               
          a0cdef                                                          
               a2cdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
a6cdef                                                                    
     abcdef                                                               
          a0cdef                                                          
               abcdef                                                     
                    a7cdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
abcde7                                                                    
     abcdef                                                               
          abcde0                                                          
               abcdef                                                     
                    abcdef                                                
                         abede5                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcde0                            
a3cdef                                                                    
     abcdef                                                               
          a0cdef                                                          
               abcdef                                                     
                    abcdef                                                
                         a1cdef                                           
                              a4cdef                                      
                                   abcdef                                 
                                        abcdef                            
a2cde2                                                                    
     abcdef                                                               
          a0cde0                                                          
               abcdef                                                     
                    a3cde3                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
abc2ef                                                                    
     abcdef                                                               
          abc0ef                                                          
               abcdef                                                     
                    abc3ef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
5bcdef                                                                    
     abcdef                                                               
          0bcdef                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   6bcdef                                 
                                        abcdef                            
333333                                                                    
     abcdef                                                               
          000000                                                          
               abcdef                                                     
                    abcdef                                                
                         111111                                           
                              444444                                      
                                   abcdef                                 
                                        abcdef                            
abcd3f                                                                    
     abcdef                                                               
          abcd0f                                                          
               abcdef                                                     
                    abcdef                                                
                         abcd1f                                           
                              abcd4f                                      
                                   abcdef                                 
                                        abcdef                            
abcde3                                                                    
     abcdef                                                               
          abcde0                                                          
               abcdef                                                     
                    abcdef                                                
                         abcde1                                           
                              abcde4                                      
                                   abcdef                                 
                                        abcdef                            
a7cdef                                                                    
     abcdef                                                               
          a0cdef                                                          
               abcdef                                                     
                    abcdef                                                
                         a5cdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        a0cdef                            
abcde5                                                                    
     abcdef                                                               
          abcde0                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcde6                                 
                                        abcdef                            
a3cde3                                                                    
     abcdef                                                               
          a0cde0                                                          
               abcdef                                                     
                    abcdef                                                
                         a1cde1                                           
                              a4cde4                                      
                                   abcdef                                 
                                        abcdef                            
abc3ef                                                                    
     abcdef                                                               
          abc0ef                                                          
               abcdef                                                     
                    abcdef                                                
                         abc1ef                                           
                              abc4ef                                      
                                   abcdef                                 
                                        abcdef                            
6bcdef                                                                    
     abcdef                                                               
          0bcdef                                                          
               abcdef                                                     
                    7bcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
444444                                                                    
     555555                                                               
          000000                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
abcd4f                                                                    
     abcd5f                                                               
          abcd0f                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
abcde4                                                                    
     abcde5                                                               
          abcde0                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
a4cde4                                                                    
     a5cde5                                                               
          a0cde0                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
abc4ef                                                                    
     abc5ef                                                               
          abc0ef                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
7bcdef                                                                    
     abcdef                                                               
          0bcdef                                                          
               abcdef                                                     
                    abcdef                                                
                         5bcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        0bcdef                            
555555                                                                    
     abcdef                                                               
          000000                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   666666                                 
                                        abcdef                            
a5cde5                                                                    
     abcdef                                                               
          a0cde0                                                          
               abcdef                                                     
                    abcdef                                                
                         abcdef                                           
                              abcdef                                      
                                   a6cde6                                 
                                        abcdef                            
666666                                                                    
     abcdef                                                               
          000000                                                          
               abcdef                                                     
                    777777                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
a6cde6                                                                    
     abcdef                                                               
          a0cde0                                                          
               abcdef                                                     
                    a7cde7                                                
                         abcdef                                           
                              abcdef                                      
                                   abcdef                                 
                                        abcdef                            
777777                                                                    
     abcdef                                                               
          000000                                                          
               abcdef                                                     
                    abcdef                                                
                         555555                                           
                              abcdef                                      
                                   abcdef                                 
                                        000000                            
a7cde7                                                                    
     abcdef                                                               
          a0cde0                                                          
               abcdef                                                     
                    abcdef                                                
                         a5cde5                                           
                              abcdef                                      
                                   abcdef                                 
                                        a0cde0                            
compl(M[1]) compl(M[2]) compl(M[3]) compl(M[4]) compl(M[5])               
 compl(M[6]) compl(M[7])                                                  
1234567S                                                                  
     abc5efg                                                              
          0000000                                                         
               2bcdefg                                                    
                    a3cde7g                                               
                         ab1def5                                          
                              ab4defg                                     
                                   abcd6fg                                
                                        abcdef0                           
abcdef0                                                                   
     abcdef1                                                              
          abedef0                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abcd6fg                                                                   
     abcdefg                                                              
          abcd0fg                                                         
               abcdefg                                                    
                    abcd7fg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
ab4defg                                                                   
     ab5defg                                                              
          ab0defg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
ab1def5                                                                   
     abcdefg                                                              
          ab0def0                                                         
               ab2defg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdef6                                
                                        abcdefg                           
a3cde7g                                                                   
     abcdefg                                                              
          a0,de0g                                                         
               abcdefg                                                    
                    abcdefg                                               
                         a1cde5g                                          
                              a4cdefg                                     
                                   abcdefg                                
                                        abcde0g                           
abc5efg                                                                   
     abcdefg                                                              
          abc0efg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abc6efg                                
                                        abedefg                           
2bcdefg                                                                   
     abcdefg                                                              
          0bcdefg                                                         
               abcdefg                                                    
                    3bcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
0000000                                                                   
     1111111                                                              
          0000000                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abcdefgE                                                                  
     abcdefg                                                              
          abcdefg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abedef1                                                                   
     abcdefg                                                              
          abcdef0                                                         
               abcdef2                                                    
                    abcdefg                                               
                         abcdefg                                          
                              ab,defg                                     
                                   abcdefg                                
                                        abcdefg                           
abcd7fg                                                                   
     abcdefg                                                              
          abcd0fg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcd5fg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcd0fg                           
abcd0fg                                                                   
     abcd1fg                                                              
          abcd0fg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
ab0defg                                                                   
     ab1defg                                                              
          ab0defg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
ab5defg                                                                   
     abcdef                                                               
          ab0defg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   ab6defg                                
                                        abcdefg                           
ab,def6                                                                   
     abcdefg                                                              
          abcdef0                                                         
               abcdefg                                                    
                    abcdef7                                               
                         abcdefg                                          
                              abedefg                                     
                                   abcdefg                                
                                        abcdefg                           
ab2defg                                                                   
     abcdefg                                                              
          ab0defg                                                         
               abcdefg                                                    
                    ab3defg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
ab0def0                                                                   
     ab1def1                                                              
          ab0def0                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abedefg                           
abcde0g                                                                   
     abcde1g                                                              
          abcde0g                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
a4cdefg                                                                   
     a5cdefg                                                              
          a0cdefg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
a1cde5g                                                                   
     abcdefg                                                              
          a0cde0g                                                         
               a2cdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcde6g                                
                                        abcdefg                           
a0cde0g                                                                   
     a1cde1g                                                              
          a0cde0g                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abedefg                                     
                                   abcdefg                                
                                        abcdefg                           
abc6efg                                                                   
     abcdefg                                                              
          abc0efg                                                         
               abcdefg                                                    
                    abc7efg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abc0efg                                                                   
     abc1efg                                                              
          abc0efg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
3bcdefg                                                                   
     abcdefg                                                              
          0bcdefg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         1bcdefg                                          
                              4bcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
0bcdefg                                                                   
     1bcdefg                                                              
          0bcdefg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
1111111                                                                   
     abcdefg                                                              
          0000000                                                         
               2222222                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abedefg                                     
                                   abcdefg                                
                                        abcdefg                           
abcdef2                                                                   
     abcdefg                                                              
          abcdef0                                                         
               abcdefg                                                    
                    abcdef3                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abcd5fg                                                                   
     abcdefg                                                              
          abcd0fg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcd6fg                                
                                        abcdefg                           
abcd1fg                                                                   
     abcdefg                                                              
          abcd0fg                                                         
               abcd2fg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
ab1defg                                                                   
     abcdefg                                                              
          ab0defg                                                         
               ab2defg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
ab6defg                                                                   
     abcdefg                                                              
          ab0defg                                                         
               abcdefg                                                    
                    ab7defg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abcdef7                                                                   
     abcdefg                                                              
          abcdef0                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdef5                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdef0                           
ab3defg                                                                   
     abcdefg                                                              
          ab0defg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         ab1defg                                          
                              ab4defg                                     
                                   abcdefg                                
                                        abcdefg                           
ab1def1                                                                   
     abcdefg                                                              
          ab0def0                                                         
               ab2def2                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abcde1g                                                                   
     abcdefg                                                              
          abcde0g                                                         
               abcde2g                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
a0cdefg                                                                   
     a1cdefg                                                              
          a0cdefg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
a5cdefg                                                                   
     abcdefg                                                              
          a0cdefg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   a6cdefg                                
                                        abcdefg                           
abcde6g                                                                   
     abcdefg                                                              
          abcde0g                                                         
               abcdefg                                                    
                    abcde7g                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
a2,defg                                                                   
     abcdefg                                                              
          a0cdefg                                                         
               abcdefg                                                    
                    a3cdefg                                               
                         abedefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
a1cde1g                                                                   
     abcdefg                                                              
          a0,de0g                                                         
               a2cde2g                                                    
                    abcdefg                                               
                         abedefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abc7efg                                                                   
     abcdefg                                                              
          abc0efg                                                         
               abedefg                                                    
                    ab,defg                                               
                         abc5efg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abc0efg                           
abc1efg                                                                   
     abcdefg                                                              
          abc0efg                                                         
               abc2efg                                                    
                    abcdefg                                               
                         abedefg                                          
                              abedefg                                     
                                   abcdefg                                
                                        abedefg                           
1bcd,fg                                                                   
     abcdefg                                                              
          0bcdefg                                                         
               2bcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
4bcdefg                                                                   
     5bcd,fg                                                              
          0bcdefg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
2222222                                                                   
     abcdefg                                                              
          0000000                                                         
               abcdefg                                                    
                    3333333                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abcdef3                                                                   
     abcdefg                                                              
          abedef0                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdef1                                          
                              abcdef4                                     
                                   abcdefg                                
                                        abcdefg                           
abcd2fg                                                                   
     abcdefg                                                              
          abcd0fg                                                         
               abcdefg                                                    
                    abcd3fg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
ab7defg                                                                   
     abcdefg                                                              
          ab0defg                                                         
               abedefg                                                    
                    abcdefg                                               
                         ab5defg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        ab0defg                           
abcdef5                                                                   
     abcdefg                                                              
          abcdef0                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdef6                                
                                        abcdefg                           
ab2d,f2                                                                   
     abcdefg                                                              
          ab0def0                                                         
               abedefg                                                    
                    ab3def3                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abed,2g                                                                   
     abcdefg                                                              
          abcd,0g                                                         
               abcdefg                                                    
                    abcde3g                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
a1cdefg                                                                   
     abcdefg                                                              
          a0cdefg                                                         
               a2cdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
a6cdefg                                                                   
     abcdefg                                                              
          a0cdefg                                                         
               abcdefg                                                    
                    a7cdefg                                               
                         abcdefg                                          
                              abedefg                                     
                                   abcdefg                                
                                        abcdefg                           
ab,de7g                                                                   
     abcdefg                                                              
          abede0g                                                         
               abcdefg                                                    
                    abcdefg                                               
                         ab,de5g                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcde0g                           
a3cdefg                                                                   
     abcdefg                                                              
          a0cdefg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         a1cdefg                                          
                              a4cdefg                                     
                                   abcdefg                                
                                        abcdefg                           
a2cde2g                                                                   
     abcdefg                                                              
          a0cde0g                                                         
               abcdefg                                                    
                    a3cde3g                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abc2efg                                                                   
     abcdefg                                                              
          abc0efg                                                         
               abcdefg                                                    
                    abc3efg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
5bcdefg                                                                   
     abcdefg                                                              
          0bcdefg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abedefg                                     
                                   6bcdefg                                
                                        abcdefg                           
3333333                                                                   
     abcdefg                                                              
          0000000                                                         
               abcdefg                                                    
                    abcdefg                                               
                         1111111                                          
                              4444444                                     
                                   abcdefg                                
                                        abcdefg                           
abcdef4                                                                   
     abcdef5                                                              
          abcdef0                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abcd3fg                                                                   
     abcdefg                                                              
          abcd0fg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcd1fg                                          
                              abcd4fg                                     
                                   abcdefg                                
                                        abcdefg                           
ab3def3                                                                   
     abcdefg                                                              
          ab0def0                                                         
               abcdefg                                                    
                    abcdefg                                               
                         ab1def1                                          
                              ab4def4                                     
                                   abcdefg                                
                                        abcdefg                           
abcde3g                                                                   
     abcdefg                                                              
          abcde0g                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcde1g                                          
                              abcde4g                                     
                                   abcdefg                                
                                        abcdefg                           
a7cdefg                                                                   
     abcdefg                                                              
          a0cdefg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         a5cdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        a0cdefg                           
abcde5g                                                                   
     abcdefg                                                              
          abcde0g                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcde6g                                
                                        abcdefg                           
a3cde3g                                                                   
     abcdefg                                                              
          a0cde0g                                                         
               abcdefg                                                    
                    abcdefg                                               
                         a1cde1g                                          
                              a4cde4g                                     
                                   abcdefg                                
                                        abcdefg                           
abc3efg                                                                   
     abcdefg                                                              
          abc0efg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abc1efg                                          
                              abc4efg                                     
                                   abcdefg                                
                                        abcdefg                           
6bcdefg                                                                   
     abcdefg                                                              
          0bcdefg                                                         
               abcdefg                                                    
                    7bcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
4444444                                                                   
     5555555                                                              
          0000000                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abcd4fg                                                                   
     abcd5fg                                                              
          abcd0fg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
ab4def4                                                                   
     ab5def5                                                              
          ab0def0                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abcde4g                                                                   
     abcde5g                                                              
          abcde0g                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
a4cde4g                                                                   
     a5cde5g                                                              
          a0cde0g                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
abc4efg                                                                   
     abc5efg                                                              
          abc0efg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
7bcdefg                                                                   
     abedefg                                                              
          0bcdefg                                                         
               abcdefg                                                    
                    abcdefg                                               
                         5bcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        0bcdefg                           
5555555                                                                   
     abcdefg                                                              
          0000000                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   6666666                                
                                        abcdefg                           
ab5def5                                                                   
     abcdefg                                                              
          ab0def0                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   ab6def6                                
                                        abcdefg                           
a5cde5g                                                                   
     abcdefg                                                              
          a0cde0g                                                         
               abcdefg                                                    
                    abcdefg                                               
                         abcdefg                                          
                              abcdefg                                     
                                   a6cde6g                                
                                        abcdefg                           
6666666                                                                   
     abcdefg                                                              
          0000000                                                         
               abcdefg                                                    
                    7777777                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
ab6def6                                                                   
     ab,defg                                                              
          ab0def0                                                         
               abcdefg                                                    
                    ab7def7                                               
                         abedefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
a6ede6g                                                                   
     abcdefg                                                              
          a0cde0g                                                         
               abcdefg                                                    
                    a7cde7g                                               
                         abcdefg                                          
                              abcdefg                                     
                                   abcdefg                                
                                        abcdefg                           
7777777                                                                   
     abcdefg                                                              
          0000000                                                         
               abcdefg                                                    
                    abcdefg                                               
                         5555555                                          
                              abcdefg                                     
                                   abcdefg                                
                                        0000000                           
ab7def7                                                                   
     abcdefg                                                              
          ab0def0                                                         
               abcdefg                                                    
                    abcdefg                                               
                         ab5def5                                          
                              abcdefg                                     
                                   abcdefg                                
                                        ab0def0                           
a7cde7g                                                                   
     abcdefg                                                              
          a0cde0g                                                         
               abcdefg                                                    
                    abcdefg                                               
                         a5cde5g                                          
                              abcdefg                                     
                                   abcdefg                                
                                        a0cde0g                           
__________________________________________________________________________
 
    
     
                                           TABLE 5                                 
__________________________________________________________________________
M[0]   comp1(M[1])   comp1(M[2])   comp1(M[3])   comp1(M[4])              
comp1(M[5])   comp1(M[6])   comp1(M[7]) = UIO(0)                          
              A/N   R/N   D/X   N/Y   B/N  C/N  N/Z  D/N                  
__________________________________________________________________________
01234567S(1)                                                              
              ##STR2##                                                    
                   00000000                                               
 ##STR3##                                                                 
             0abc0efg                                                     
                    ##STR4##                                              
00000000     11111111                                                     
                   00000000                                               
 ##STR5##                                                                 
             0abcdefg                                                     
              ##STR6##                                                    
0abc0efg     1abc1efg                                                     
                   0abc0efg                                               
11111111                                                                  
             00000000                                                     
                   22222222                                               
 ##STR7##                                                                 
              ##STR8##                                                    
             1abcdefg                                                     
                   4abcdefg                                               
 ##STR9##                                                                 
              ##STR10##                                                   
                   0abcdefg                                               
1abc1efg                                                                  
             0abc0efg                                                     
                   2abc2efg                                               
22222222                                                                  
             00000000                                                     
             33333333                                                     
 ##STR11##                                                                
             0abcdefg                                                     
                   2abcdefg                                               
4abcdefgE    5abcdefg                                                     
                   0abcdefg                                               
2abc2efg                                                                  
             0abc0efg                                                     
             3abc3efg                                                     
33333333                                                                  
             00000000                                                     
             11111111                                                     
                   44444444                                               
5abcdefgE                                                                 
             0abcdefg                                                     
             6abcdefg                                                     
3abc3efg                                                                  
             0abc0efg                                                     
             1abc1efg                                                     
                   4abc4efg                                               
44444444     55555555                                                     
                   00000000                                               
6abcdefgE                                                                 
             0abcdefg                                                     
             7abcdefg                                                     
4abc4efg     5abc5efg                                                     
                   0abc0efg                                               
55555555                                                                  
             00000000                                                     
             66666666                                                     
7abcdefgE                                                                 
             0abcdefg                                                     
             5abcdefg                                                     
             0abcdefg                                                     
5abc5efg                                                                  
             0abc0efg                                                     
             6abc6efg                                                     
66666666                                                                  
             00000000                                                     
             77777777                                                     
6abc6efg                                                                  
             0abc0efg                                                     
             7abc7efg                                                     
77777777                                                                  
             00000000                                                     
             55555555                                                     
             00000000                                                     
7abc7efg                                                                  
             0abc0efg                                                     
             5abc5efg                                                     
             0abc0efg                                                     
__________________________________________________________________________
 
    
     
                                           TABLE 6                                 
__________________________________________________________________________
M[7]  comp1(M[0])   comp1(M[1])    comp1(M[2])   comp1(M[3])              
comp1(M[4])   comp1(M[5])   comp1(M[6]) = UIO(7)                          
              A/N  R/N  D/X  N/Y  B/N   C/N  N/Z  D/N                     
__________________________________________________________________________
 ##STR12##                                                                
             00000000                                                     
              ##STR13##                                                   
              ##STR14##                                                   
 ##STR15##                                                                
             0abc0efg                                                     
              ##STR16##                                                   
 ##STR17##   1abcdefg                                                     
                  0abcdefg                                                
00000000     11111111                                                     
                  00000000                                                
 ##STR18##                                                                
             0abcdefg                                                     
             7abcdefg                                                     
0abc0efg     1abc1efg                                                     
                  0abc0efg                                                
1abcdefgE                                                                 
             0abcdefg                                                     
                  2abcdefg                                                
11111111                                                                  
             00000000                                                     
                  22222222                                                
7abcdefgE                                                                 
             0abcdefg                                                     
             5abcdefg                                                     
             0abcdefg                                                     
1abc1efg                                                                  
             0abc0efg                                                     
                  2abc2efg                                                
2abcdefgE                                                                 
             0abcdefg                                                     
             3abcdefg                                                     
22222222                                                                  
             00000000                                                     
             33333333                                                     
5abcdefgE                                                                 
             0abcdefg                                                     
             6abcdefg                                                     
2abc2efg                                                                  
             0abc0efg                                                     
             3abc3efg                                                     
3abcdefgE                                                                 
             0abcdefg                                                     
             1abcdefg                                                     
                  4abcdefg                                                
33333333                                                                  
             00000000                                                     
             11111111                                                     
                  44444444                                                
3abc3efg                                                                  
             0abc0efg                                                     
             1abc1efg                                                     
                  4abc4efg                                                
4abcdefgE    5abcdefg                                                     
                  0abcdefg                                                
44444444     55555555                                                     
                  00000000                                                
4abc4efg     5abc5efg                                                     
                  0abc0efg                                                
55555555                                                                  
             00000000                                                     
             66666666                                                     
5abc5efg                                                                  
             0abc0efg                                                     
             6abc6efg                                                     
66666666                                                                  
             00000000                                                     
             77777777                                                     
6abc6efg                                                                  
             0abc0efg                                                     
             7abc7efg                                                     
77777777                                                                  
             00000000                                                     
             55555555                                                     
             00000000                                                     
7abc7efg                                                                  
             0abc0efg                                                     
             5abc5efg                                                     
             0abc0efg                                                     
__________________________________________________________________________
 
    
     
                                           TABLE 7                                 
__________________________________________________________________________
A/X      A/Y  A/Z  B/X  B/Y  B/Z  C/Y                                     
__________________________________________________________________________
M[1] = M                                                                  
1S  1    --   --   --   --   --   4                                       
2E  --   1    --   3    --   --   --                                      
3E  --   5    --   --   --   --   --                                      
4E  5    --   --   --   --   3    --                                      
5E  --   --   1    --   2    --   5                                       
compl(M[2])                                                               
aE  a    a    a    a    a    a    a                                       
1   1    a    a    a    a    a    4                                       
2S  a    1    1    3    a    a    a                                       
3   a    5    a    1    a    a    a                                       
4   5    a    a    a    a    3    a                                       
5   a    a    1    a    2    a    5                                       
compl(M[3])                                                               
bE  b    b    b    b    b    b    b                                       
1   1    b    b    b    b    b    4                                       
2   b    1    b    3    b    b    b                                       
3S  b    5    b    b    b    b    b                                       
4   5    b    b    b    b    3    b                                       
5   b    b    1    b    2    b    5                                       
compl(M[4])                                                               
cE  c    c    c    c    c    c    c                                       
1   1    c    c    c    c    c    4                                       
2   c    1    c    3    c    c    c                                       
3   c    5    c    c    c    c    c                                       
4S  5    c    c    c    c    3    c                                       
5   c    c    1    c    2    c    5                                       
compl(M[5])                                                               
dE  d    d    d    d    d    d    d                                       
1   1    d    d    d    d    d    4                                       
2   d    1    d    3    d    d    d                                       
3   d    5    d    d    d    d    d                                       
4   5    d    d    d    d    3    d                                       
5S  d    d    1    d    2    d    5                                       
compl(M[2]) compl(M[3])                                                   
23S ab   15   ab   3b   ab   ab   ab                                      
abE ab   ab   ab   ab   ab   ab   ab                                      
15  1b   ab   a1   ab   a2   ab   45                                      
3b  ab   5b   ab   ab   ab   ab   ab                                      
a2  ab   a1   ab   a3   ab   ab   ab                                      
a1  a1   ab   ab   ab   ab   ab   a4                                      
1b  1b   ab   ab   ab   ab   ab   4b                                      
45  5b   ab   a1   ab   a2   3b   a5                                      
5b  ab   ab   1b   ab   2b   ab   5b                                      
a3  ab   a5   ab   ab   ab   ab   ab                                      
a4  a5   ab   ab   ab   ab   a3   ab                                      
4b  5b   ab   ab   ab   ab   3b   ab                                      
a5  ab   ab   a1   ab   a2   ab   a5                                      
2b  ab   1b   ab   3b   ab   ab   ab                                      
compl(M[2]) compl(M[3]) compl(M[4])                                       
234S                                                                      
    ab5  15c  abc  3bc  abc  ab3  abc                                     
abcE                                                                      
    abc  abc  abc  abc  abc  abc  abc                                     
ab3 abc  ab5  abc  abc  abc  abc  abc                                     
ab5 abc  abc  ab1  abc  ab2  abc  ab5                                     
15c 1bc  abc  a1c  abc  a2c  abc  45c                                     
3bc abc  5bc  abc  abc  abc  abc  abc                                     
ab2 abc  ab1  abc  ab3  abc  abc  abc                                     
ab1 ab1  abc  abc  abc  abc  abc  ab4                                     
a2c abc  a1c  abc  a3c  abc  abc  abc                                     
a1c a1c  abc  abc  abc  abc  abc  a4c                                     
1bc 1bc  abc  abc  abc  abc  abc  4bc                                     
45c 5bc  abc  a1c  abc  a2c  3bc  a5c                                     
5bc abc  abc  1bc  abc  2bc  abc  5bc                                     
ab4 ab5  abc  abc  abc  abc  ab3  abc                                     
a3c abc  a5c  abc  abc  abc  abc  abc                                     
a4c a5c  abc  abc  abc  abc  a3c  abc                                     
4bc 5bc  abc  abc  abc  abc  3bc  abc                                     
a5c abc  abc  a1c  abc  a2c  abc  a5c                                     
2bc abc  1bc  abc  3bc  abc  abc  abc                                     
compl(M[2]) compl(M[3]) compl(M[4]) compl(M[5])                           
2345S                                                                     
    ab5d 15cd abc1 3bcd abc2 ab3d abc5                                    
abc5                                                                      
    abcd abcd abc1 abcd abc2 abcd abc5                                    
ab3d                                                                      
    abcd ab5d abcd abcd abcd abcd abcd                                    
abc2                                                                      
    abcd abc1 abcd abcs abcd abcd abcd                                    
abc1                                                                      
    abc1 abcd abcd abcd abcd abcd abc4                                    
ab5d                                                                      
    abcd abcd ab1d abcd ab2d abcd ab5d                                    
15cd                                                                      
    1bcd abcd a1cd abcd a2cd abcd 45cd                                    
3bcd                                                                      
    abcd 5bcd abcd abcd abcd abcd abcd                                    
abcdE                                                                     
    abcd abcd abcd abcd abcd abcd abcd                                    
abcs                                                                      
    abcd abc5 abcd abcd abcd abcd abcd                                    
abc4                                                                      
    abc5 abcd abcd abcd abcd abcs abcd                                    
ab2d                                                                      
    abcd ab1d abcd ab3d abcd abcd abcd                                    
ab1d                                                                      
    ab1d abcd abcd abcd abcd abcd ab4d                                    
a2cd                                                                      
    abcd a1cd abcd a3cd abcd abcd abcd                                    
a1cd                                                                      
    a1cd abcd abcd abcd abcd abcd a4cd                                    
1bcd                                                                      
    1bcd abcd abcd abcd abcd abcd 4bcd                                    
45cd                                                                      
    5bcd abcd a1cd abcd a2cd 3bcd a5cd                                    
5bcd                                                                      
    abcd abcd 1bcd abcd 2bcd abcd 5bcd                                    
ab4d                                                                      
    ab5d abcd abcd abcd abcd ab3d abcd                                    
a3cd                                                                      
    abcd a5cd abcd abcd abcd abcd abcd                                    
a4cd                                                                      
    a5cd abcd abcd abcd abcd a3cd abcd                                    
4bcd                                                                      
    5bcd abcd abcd abcd abcd 3bcd abcd                                    
a5cd                                                                      
    abcd abcd a1cd abcd a2cd abcd a5cd                                    
2bcd                                                                      
    abcd 1bcd abcd 3bcd abcd abcd abcd                                    
M[1] compl(M(8 2]) compl(M[3]) compl(M[4]) compl(M[5]) = UIO[1]           
12345                                                                     
    1ab5d                                                                 
         --   --   --   --   --   4abc5                                   
1ab5d                                                                     
    1abcd                                                                 
         --   --   --   --   --   4ab5d                                   
abc5                                                                      
    5abcd                                                                 
         --   --   --   --   3abcd                                        
                                  --                                      
1abcdE                                                                    
    1abcd                                                                 
         --   --   --   --   --   4abcd                                   
ab5d                                                                      
    5abcd                                                                 
         --   --   --   --   3abcd                                        
                                  --                                      
abcdE                                                                     
    --   --   1abcd                                                       
                   --   2abcd                                             
                             --   5abcd                                   
abcdE                                                                     
    --   5abcd                                                            
              --   --   --   --   --                                      
abcdE                                                                     
    5abcd                                                                 
         --   --   --   --   3abcd                                        
                                  --                                      
abcdE                                                                     
    --   1abcd                                                            
              --   3abcd                                                  
                        --   --   --                                      
__________________________________________________________________________
 
    
     
                                           TABLE 8                                 
__________________________________________________________________________
;THE SIGNATURE (UIO, SIOS) ALGORIRITHM                                    
;S.P. van de Burget                                                       
;(c) 1990-1992 PTT Research                                               
;P.0 Box 421, Leidschendam                                                
;the Netherlands                                                          
;Functions of interest                                                    
;(signature FA S)    competes the signature FA of an FA                   
;(shortest-path FA)    computes a shortest path from start to some end    
state                                                                     
;(collect-paths FA)    computes all non-cyclic shortest paths to some end 
state                                                                     
;(print-list L)    prints a list, one item per line                       
;(print-fa FA)    pretty prints the FA                                    
;(restart-fa FA S)    computes a FA with a new start state S              
;(isect-ff FAL FA2)    computes the intersection of two FAs               
;(compl-fa FA)    compute the complement of an FA                         
;Examples con be found at the end of this file                            
(defmacro foreach (var in set where cond &amp;body body)                      
 &#39;(do ((1st, set (rest 1st)) (,var))                                      
   ((null 1st))                                                           
  (setq var (car 1st))                                                    
  (con (,cond                                                             
    ,@body))))                                                            
(defun isect-fa (M1 M2)                                                   
 (let ((Q1 (first M1)) (Q2 (first M2)) (Q3 nil)                           
   A (second M1))                                                         
   (d1 (third M1)) (d2 (third M2)) (d3 nil)                               
   (s1 (fourth M1)) (s2 (fourth M2)) (s3 nil)                             
   (F1 (fifth M1)) (F2 (fifth M2)) (F3 nil))                              
  (setq s3 (list s1 s2))                                                  
  (setq Q3 (list s3))                                                     
  (do ((mark Q3 (rest mark)) (p) (q))                                     
   ((null mark)                                                           
   (list Q3 A d3 s3 F3))                                                  
   setq p (car (first mark)))                                             
   setq q (cadr (first mark))) ; was cdr, moet second?                    
   foreach al in d1 where (equal (car al) p) ; of first 7?                
    (foreach a2 in d2 where (and (equal (first a2) q                      
          (equal (second a2) (second a1)))                                
     (let* ((ostate (list p q))                                           
       (nstate list (third a1) (third a2)))                               
       (ntrans (list ostate (second a1) nstate)))                         
     (cond ((not (member nstate Q3 :test &#39;equal))                         
       (setq Q3 (nconc Q3 (list nstate)))))                               
      (cond ((not (member ntrans d3 :test &#39;equal))                        
        (setq d3 (nconc d3 (list ntrans)))))                              
     (cond ((and (member (third a1) F1 ;test &#39;equal)                      
        (member (third a2) F2 :test &#39;equal)                               
        (not (member nstate F3 ;test &#39;equal)))                            
       (setq F3 (nconc F3 (list nstate)))))))))))                         
(defun compl-fa (M)                                                       
  (let ((Q (first M)) (A (second M)) (d (third M)) (q0 (fourth M))        
   (tau (gensym))                                                         
   (nQ (first M)) (nd (third M))                                          
   (nF (my-set-diff (first M) (fifth M))))                                
  (setq nQ (cons tau nQ))                                                 
  (setq nF (cons tau nF))                                                 
  (foreach a in A where t                                                 
     (foreach q in Q where (not (outgoing q a d))                         
        (setq nd (cons (list q a tau) nd)))                               
     (setq nd (cons (list tau a tau) nd)))                                
  (list nQ A nd q0 nF)))                                                  
(defun outgoing (q a delta)                                               
  (cond                                                                   
  ((null delta) nil)                                                      
  ((and (equal (caar delta) q) (equal (cadar delta) a)) (caddar delta)) ; 
  (t (outgoing q a (rest delta)))))                                       
(defun restart-fa (M q)                                                   
 (cond                                                                    
(Is continuated)                                                          
  ((member q (first M) ;test &#39;equal)                                      
   (list (first M) (second M) (third M) q (fifth M)))))                   
(defun signature (M q)                                                    
  (do ((qq (my-set-diff (first M) (list q))                               
     (rest qq))                                                           
    (restart-fa M q)))                                                    
   ((null qq) nM)                                                         
  (setq nM (isect-fa nM (compl-fa (restart-fa M (first qq)))))))          
;find a shortest path from start state to some end state                  
(defun shortest-path (M)                                                  
 (reverse (do-shortest (third M) (list (list (fourth M))) (fifth M))))    
(defun do-shortest (arcs paths final)                                     
 (let ((newpaths nil) (found nil))                                        
  (foreach p in paths where t                                             
     (foreach a in arcs where (equal (first a) (first p))                 
      (setq newpaths                                                      
       (cons (cons (third a) (cons (second a) (rest p)))                  
        newpaths))                                                        
       (cond                                                              
       ((member (third a) final :test &#39;equal)                             
        (setq found (cons (second a) (rest p)))))))                       
  (cond                                                                   
   ((not found) (do-shortest arcs newpaths final))                        
   (t found))))                                                           
;collect all non-cyclic shortest path                                     
(defun collect-paths (M)                                                  
 (reverse (do-collect M (fourth M) nil nil)))                             
(defun do-collect (M a visited rseq)                                      
 (let ((uio-a nil))                                                       
  (foreach a in (third M) where (equal (first a) s)                       
     (cond                                                                
      ((member (third a) visited)                                         
      t)                                                                  
(Is continuated)                                                          
      ((member (third a) (fifth M) :test &#39;equal)                          
       (setq uio-s (cons (reverse (cons (second a) rseq)) uio-s)))        
      (t                                                                  
       (setq uio-s                                                        
        (append (do-collect M (third a)                                   
          (con s visited)                                                 
          (cons (second a) rseq))                                         
          uio-s)))))                                                      
  uio-s))                                                                 
(defun print-list (1)                                                     
 (foreach e in 1 where t                                                  
    (princ e)                                                             
    (terpri))                                                             
 t)                                                                       
(defun print-fa (M)                                                       
 (terpri)                                                                 
(foreach a in (second M) where t                                          
    (princ &#39;|  |) (princ a))                            
 (terpri)                                                                 
 (foreach s in (first M) where t                                          
    (print-dotted s)                                                      
     (print-marker M s)                                                   
    (foreach a in (second M) where t                                      
       (princ &#39;|  |)                                    
       (print-dotted (nil-to-dash (outgoing s a (third M)))))             
    (terpri)) t)                                                          
(defun print-marker (M s)                                                 
 (cond                                                                    
  ((equal s (fourth M))                                                   
   (cond                                                                  
    ((member a (fifth M) :test &#39;equal) (princ &#39;|*|))    
    (t (princ &#39;| |))))                                  
  ((member s (fifth M) :test &#39;equal) (princ &#39;|#|))      
(Is continuated)                                                          
(defun print-dotted (L)                                                   
 (cond                                                                    
  ((null L))                                                              
  ((atom L) (princ L) (princ &#39;|.|))                     
  ((listp L) (print-dotted (car L)) (print-dotted (cdr L)))))             
(defun nil-to-dash (C)                                                    
 (cond                                                                    
  ((null C) &#39;|-|)                                       
  (t C)))                                                                 
; Common lisp functions, uncomment if needed                              
(defun my-set-diff (P Q)                                                  
 (set-difference P Q :test &#39;equal))                                       
; (cond                                                                   
; ((null P) nil)                                                          
; ((member (first Q) P :test &#39;equal) (my-set-diff (rest P) Q))            
; (t (cons P (my-set-diff (rest P) Q)))))                                 
;(defun first (L)                                                         
; (car L))                                                                
;(defun second (L)                                                        
; (cadr L))                                                               
;(defun third (L)                                                         
; (caddr L))                                                              
;(defun fourth (L)                                                        
; (cadddr L))                                                             
;(defun fifth (L)                                                         
; (caddddr L))                                                            
;Some example machines                                                    
;syntax: (States+Alphabet+Transitions+StartState EndState+)               
;all fie a marked with + are lists and each element of Transitions        
;has syntax: (FromState Input ToState)                                    
(Is continuated)                                                          
(setq M1 &#39;((P1 P2 P3) (A B C)                                             
      ((P1 A P2) (P2 B P2) (P2 C P3)) P1 (P3))) ; ab*c                    
(setq M2 &#39;((P1 P2 P3) (A B C)                                             
      ((P1 A P2) (P2 B P2) (P2 A P3) (P2 B P3) (P2 C P3)) P1 (P3))) ;     
ab*.                                                                      
(setq M3 &#39;((P1 P2 P3) (A B C)                                             
      ((P1 A P2) (P2 C P3)) P1 (P2 P3))) ; a[c]                           
(setq M4 &#39;((P1 P2 P3 P4) (A B C)                                          
      ((P1 A P2) (P2 C P4) (P2 B P3) (P3 C P4)) P1 (P4))) ; a[b]c         
;Paper example                                                            
(setq vb &#39;((1 2 3) (a/x a/y b/x b/y)                                      
      ((1 a/x 2) (1 b/y 1) (2 a/y 3) (2 bly 2) (3 a/x 1) (3 b/x 3))       
      1 (1 2 3)))                                                         
; pat 4.692.921 example                                                   
(setq patl &#39;((0 1 2 3 4 5 6 7) (a/null r/null d/x null/ b/null c/null     
null/z d/null)                                                            
      ((0 a/null 1) (1 d/x 2) (2 null/y 3) (3 b/null 1) (3 c/null 4)      
      (4 a/null 5) (5 null/z 6) (6 null/y 7) (7 b/null 5) (7 d/null 0)    
      (0 r/null 0) (1 r/null 0) (2 r/null 0) (3 r/null 0) (4 r/null 0)    
       (5 r/null 0) (6 r/null 0) (7 r/null 0))                            
      0 (0 1 2 3 4 5 6 7)))                                               
; pat 4.991.176 example                                                   
(setq pat2 &#39;((S1 S2 S3 S4 S5) (a/x a/y a/z b/x b/y b/z c/y)               
      ((S1 a/x S1) (S1 c/y S4) (S2 a/y S1) (S2 b/z S3)                    
      (S3 a/y S5) (S4 a/x S5) (s4 b/z S3)                                 
      (S5 c/y S5) (S5 b/y S2) (S5 a/z S1)                                 
      )                                                                   
      S1 (S1 S2 S3 S4 S5)))                                               
(princ &#34;the Signature algorithm&#34;)(terpri)                                 
(princ &#34;&#34;by Stan van de Burgt&#34;)(terpri)                                   
(princ &#34;(c) 1990-1992 PTT Research&#34;)(terpri)                              
T                                                                         
(Is continuated)                                                          
__________________________________________________________________________