Patent Publication Number: US-5299206-A

Title: System and method for analyzing complex sequences in trace arrays using multiple finite automata

Description:
FIELD OF THE INVENTION 
     The present invention relates to systems and methods that are useful in analyzing computer trace arrays. More specifically, the present invention relates to systems and methods that are useful in analyzing complex sequences of events in trace arrays using multiple finite automata. 
     BACKGROUND OF THE INVENTION 
     In the development of new electronic products, it is necessary to test and debug both the hardware and software of these products. These testing and debugging operations are key factors to bringing new products to market. 
     To perform these testing and debugging operations on computers or digital circuits, engineers frequently use an instrument called a &#34;logic analyzer.&#34; In its most common use, a logic analyzer periodically samples (or captures) and stores the states of several digital signals at the same time. 
     In use, a logic analyzer records or &#34;traces&#34; the behavior of the computer or digital circuit over a period of time. To do this, the logic analyzer is periodically activated to sample the states of a predetermined number of digital signals. 
     The record of the computer&#39;s or digital circuit&#39;s behavior over a prescribed period of time is referred to as a &#34;logic trace.&#34; Such an array may also be referred to as a &#34;logic trace array&#34; or simply a &#34;trace array&#34;. Since this array only contains &#34;0s&#34; and &#34;1s,&#34; a trace array also may be referred to as a &#34;binary array.&#34; Although there may be various ways of organizing the trace array, a preferred method is a two dimensional array such as the representative prior art trace array shown in FIG. 1. 
     In FIG. 1, the representative trace array is shown generally at 100. Each entry in the array is either &#34;1&#34; or &#34;0,&#34; and represents the state of one digital signal from a computer or other digital circuit at one point in time. The trace array at 100 has representative rows 102, 104, 106, 108, 110 and 112, and representative columns 114, 116, 118, 120, 122, and 124. 
     In the trace array at 100, all of the entries for one signal are in a single column in the order in which sampling takes place. This is so each column traces the behavior of one particular digital signal over time. Each row contains the state of all the signals at one particular point in time. As such, a row is a &#34;sample&#34; of all the signals at a particular point in time. 
     For many years, logic analyzers could collect only small arrays such as that shown in FIG. 1. That is, logic analyzers could only store arrays having up to 4,096 to 8,192 samples (rows) and 48 to 64 signals (columns). Arrays of this size could be printed out on paper and then analyzed by hand to understand the circuit behavior recorded in the trace array. This permitted desired signal patterns to be viewed and evaluated with little trouble for their frequency and affect on the computer or digital circuit being tested. 
     It has been found that the usefulness of logic trace arrays of the size shown in FIG. 1 is limited for testing and debugging purposes because such traces cover only a very small time window of sampled data. Therefore, in many cases, very complex circuit problems could not be solved using these small size trace arrays. Hence, it is desirable to have a much larger time window of captured data for analyzing more complex circuit behavior and a method to analyze larger trace arrays that provide larger time windows. 
     Today, we have logic analyzers that generate much larger trace arrays than that shown in FIG. 1. These new powerful tools provide much larger time windows for data acquisition for sampling the behavior of computers or digital circuits. For example, logic analyzers now have been built to collect trace arrays as large as 524,288 samples of 192 signals, or 2,097,152 samples of 64 signals. These trace arrays, however, are too large to print out on paper and analyzer by hand. There is a need for a practical and an efficient way to analyze these larger trace arrays that heretofore has not been available. A consideration may be to look to known pattern searching methods such as those used for searching text files. 
     A known method for searching for particular patterns in text files is to define the desired pattern as a regular expression. From the regular expression, a finite automaton is generated. The finite automaton then is used to search the text file for the desired pattern. 
     Regular expressions are a useful way to describe the kinds of patterns engineers search for when analyzing trace arrays. Furthermore, using finite automata generated from regular expressions is an efficient technique for pattern searching. 
     A regular expression is compiled into a recognizer that is used for pattern searching by constructing a transition diagram that is called a finite automaton. A recognizer is a program that takes an input string and answers &#34;yes&#34; if the string matches a pattern specified by a regular expression and &#34;no&#34; otherwise. A transition diagram or finite automaton depicts the actions that take place in the recognizer in the acquisition of tokens. A token is a sequence of characters having a collective meaning. 
     FIG. 2 shows a prior art method for searching text files in the above described manner and FIG. 3 shows an apparatus for implementing this method. Referring to FIG. 2, the prior art searching method is shown generally at 200. At step 1 at 210, regular expressions that define the patterns to be searched for are input to an appropriate apparatus designed and configured to conduct the search. At step 2 at 220, the regular expressions that are input to the apparatus are used to generate conventional finite automata. Step 3 at 230 is where the text file to be searched is input to the apparatus capable of conducting the search. This also is where the text file is searched for the desired patterns. Following this, at step 4 at 240, the results of the search are output from the searching apparatus. 
     Referring to the FIG. 3, a block diagram of the system for implementing the method of FIG. 2 is shown generally at 250. The regular expressions based on the patterns to be searched for are input to the apparatus at regular expression input 251 and then placed on line 252. The regular expressions constitute the first input to system 250. 
     The regular expressions on line 252 are input to generator 254 that generates conventional finite automata from these regular expressions. The conventional finite automata are output from generator 254 on line 256. The finite automata just generated are input to analyzer 260. 
     The second input to system 250 is the text file that is to be searched. It is input at text file input 257. The text file input connects to line 258, so the text file on line 258 is input to analyzer 260. Analyzer 260 uses the conventional finite automata to search the text file for patterns. The results of the search are output from analyzer 260 on line 262. 
     Lexical analyzers used in compilers often use an extension of this method to search text files. Lexical analyzers combine the finite automata from several regular expressions into a single finite automaton to partition the text file into a series of tokens. Each character of the text file is placed into exactly one token. No character is ever placed in two or more tokens. Therefore, no two tokens in the series overlap. The techniques of the prior art may be applied to trace arrays by considering tokens as events. Hence, a series of tokens may be viewed as a series of nonoverlapping events. 
     These methods of handling text files discussed above are discussed in Aho et al., &#34;Chapter 3: Lexical Analysis,&#34; Compilers: Principles, Techniques, and Tools, Addison-Wesley, 1986, and other sections of this text. 
     Trace arrays, which include the continuum of trace array sizes from small and conventional to large, often contain one or more series of overlapping events. That is, many trace arrays contain a single series of overlapping events or several parallel series of overlapping events. For example, a computer bus that is being analyzed may have two sets of signals: data signals and arbitration signals. On such a bus, the situation may arise where during a data transfer on the data signals, the arbitration signals may be determining which bus device will own the bus after that data transfer completes. Hence, two separate but related events are occurring simultaneously. Known searching techniques do not have an ability to analyze such complex overlapping sequences of events as this. 
     Referring now generally to the treatment of text files in the past, text files have been treated as a string of symbols. These symbols are based on alphabets of finite size. For example, a text file that is input on line 258 of system shown in FIG. 3 may be an ASCII text file. Each ASCII character of the ASCII character set is treated as one symbol. The ASCII character set is a finite alphabet that contains 128 characters as will be shown. 
     A finite automaton as it has been used in the prior art consists of: 
     1. A set of states &#34;s.&#34; 
     2. A finite set of input symbols that constitutes the input symbol alphabet. 
     3. A transition function that maps state-symbol pairs to sets of states. 
     4. A state &#34;s 0  &#34; which is the start state. 
     5. A set of states &#34;F&#34; that are the accepting states. 
     In FIG. 4, an example of a finite automaton represented in a transition graph for the regular expression (a|b)*abb is shown generally at 275. In that Figure, the nodes are the states and the labeled edges are transitions. 
     The regular expression (a|b)*abb is the set of all strings of a&#39;s or b&#39;s ending in abb. In defining the finite automaton as represented in the transition graph of FIG. 4, the set of states are {0, 1, 2, 3}, the input symbol alphabet is {a,b}, the start state is s 0 , and the accepting state is s 3 . The transition function may be represented by the transition table at Table 1. 
     
                       TABLE 1                                                     
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            Input                                                         
            Alphabet Symbol                                               
State         a        b                                                  
______________________________________                                    
0             {0,1}    {0}                                                
1             --       {2}                                                
2             --       {3}                                                
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     A transition function as used in this capacity specifies for each transition function pair (s,a), where &#34;s&#34; is a state of the finite automaton and a is a particular symbol of the finite input alphabet, the next state of the finite automaton. Consider, for example, a finite automaton with the transition function f(s,a). If the finite automaton is in state &#34;s 1  &#34; and reads input symbol a, and f(s 1 ,a)=s 2 , then the finite automaton will go to state s 2 . 
     In the prior art, it has been important that the symbols for use with a finite automaton come from a finite alphabet. If they do not and come from an input alphabet of infinite size, the transition function also will be of an infinite size; and as such, a system such as that shown at 250 (FIG. 3) could not implement the transition function. As will now be shown, even though a large trace array may be presented in the same manner as text files, it does not mean that these large trace arrays may be analyzed in the same manner as conventional text files because of the inability of the prior art methods to be able to use infinite alphabets. 
     A representative ASCII file will now be discussed to demonstrate the inability of prior art text file searching methods to search or analyze larger trace arrays. In ASCII text files, each ASCII character is represented by a 7-bit code. For the purpose of this example, the ASCII text file contains 100 characters. The text file, therefore, may be represented by a binary array containing 100 rows and 7 columns. Each row may store a single character from the text file; and, thus, each row may represent a single symbol of the input alphabet. The first character of the text file goes in the first row of the array, the second character goes in the second row, and so on for the 100 characters. Hence, reading the array from the first to the last row is the same as scanning the text file from beginning to end. 
     Now, consider representing a large trace array as a text file. If a trace array contains 192 columns and 524,288 rows, in the text file context, each row will represent one character of a character set. Thus, the trace array may be presented as a text file containing 524,288 characters and each character has a 192-bit code. 
     In analyzing conventional text files, a first given is that the text file uses a finite alphabet. The ASCII character set that uses a 7-bit code per character will have 2 7  or 128 characters in that set. Such a text file is shown in FIG. 5 at 280. This text file has representative rows 281, 282, 283, 284, 285, 286, and 287; and representative columns 288, 289, 290, 291, 292, 293, and 294. The transition function is relatively easy to implement for finite automata using this ASCII character set as an input symbol alphabet. 
     On the other hand, the character set for the large trace array discussed above has a 192-bit code for each character. As would be known, the character set using 192-bit codes would contain 2 192  or 6,277,101,735,386,680,763,835,789,423,207,666,416,102,355,444,464,034,512,896 characters, which for all practical purposes is an infinite character set. Given this character set size, it would be extremely difficult, if not impossible, to implement a transition function for a finite automaton using such a character set as an input symbol alphabet. 
     The present invention overcomes the problems that have been described and provides a system and method to automatically and efficiently analyze large trace arrays, and a system and method that overcome the overlapping token restriction problem in trace arrays of any size. 
     SUMMARY OF THE INVENTION 
     The present invention is a system and method for analyzing large trace arrays, for example, trace arrays that approach the size of 192 columns (signals) and 524,288 rows (samples), or 64 columns (signals) and 2,097,152 rows (samples), and for analyzing trace arrays in general using multiple finite automata to handle complex sequences of events, such as overlapping events. 
     In order to be able to search and analyze logic trace arrays of this size (which far exceed the limits of conventional finite alphabets), the system and method of the present invention make use of finite automata that use arithmetic/logic expressions, instead of symbols, that enable the use of a substantially infinite alphabet. More specifically, the transition function that is used with a finite automaton specifies for each transition function pair (state-expression), what the next state is, but the transition function does so by using arithmetic/logic expressions rather than input symbols from a finite alphabet; thereby overcoming restrictions in prior art systems and methods to only use a finite alphabet. 
     The use of arithmetic/logic expressions with finite automata permits the automatic and efficient searching, and analysis of large trace arrays that heretofore were difficult, if not impossible, to search with conventional text file searching methods. The finite automata that use arithmetic/logic expressions as described are used in the system and method of the present invention to give engineers the tools to craft specifically tailored searches to obtain the desired information from large trace files. 
     To handle complex overlapping sequences of events, the regular expressions are not converted to a single finite automaton but to multiple finite automata. The regular expressions for each finite automaton are then grouped together. When the trace array is searched, it is searched simultaneously with multiple finite automata to obtain the desired result. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows a representative conventional prior art trace array that has 48 to 64 signals (columns) and 4,096 to 8,192 samples (rows). 
     FIG. 2 shows the steps of a prior art method for searching text files. 
     FIG. 3 is a block diagram of a prior art system implementing the prior art method shown in FIG. 2. 
     FIG. 4 is a transition graph for a finite automaton that recognizes the regular expression (a|b)*abb. 
     FIG. 5 is a representative prior art ASCII text file. 
     FIG. 6 shows a representative large trace array that now is able to be searched using the system and method of the present invention. 
     FIG. 7A is a representative timing diagram for four representative signals that are part of a larger number of signals. 
     FIG. 7B is a trace array for the signals shown in FIG. 7A. 
     FIG. 8 shows the steps of a method of the present invention. 
     FIG. 9 is a block diagram of the system of the present invention that implements the method shown in FIG. 8. 
     FIG. 10 is a timing diagram for signals that have an overlapping problem. 
     FIG. 11 is a trace array for a 64 bit wide trace that includes three extra columns that are used for communications among the multiple finite automata. 
     FIG. 12 shows the steps of a method of the present invention when multiple finite automata are generated and used. 
     FIG. 13 is a block diagram of a system of the present invention that implements the method shown in FIG. 12. 
    
    
     BEST MODE FOR CARRYING OUT THE PRESENT INVENTION 
     The present invention is a system and method that are useful for searching and analyzing large trace arrays, and for searching and analyzing trace arrays of any size if they have overlapping events. 
     Referring to FIG. 6, a representative large trace array of the type that may be automatically and efficiently searched and analyzed using the system and method of the present invention is shown generally at 300. Large trace array 300 has representative rows 302, 304, 306, 308, 310, and 312 of the total number which may range from 524,288 to 2,097,152. The rows represent the number of samples that are taken of all signals. The large trace array also has representative columns 314, 316, 318, 320, 322, and 324 of the total number which may range from 64 to 192. The columns represent the number of signals that are sampled at a given point in time. 
     According to the present invention, the finite automata that are generated from the regular expressions consist of the following: 
     1. A set of states &#34;s.&#34; 
     2. A set of arithmetic/logic expressions (which permit use of a substantially infinite alphabet). 
     3. A transition function that maps the state-arithmetic/logic expression pair to sets of states. 
     4. A starting state. 
     5. An accepting state. 
     As should be noted, the transition function immediately above is different from the transition function defined by f(s,a). The transition function of the finite automata following the present invention specifies for each transition function pair, what the next state of a finite automaton will be based on (s,e), where &#34;s&#34; is the state of the finite automaton and e is an arithmetic/logic expression. 
     The use in the transition function of the present invention of e, an arithmetic/logic expression, instead of a, a particular symbol of the finite input alphabet, permits an expansion of the transition function to embrace the use of an infinite alphabet. Therefore, for example, considering a finite automaton with a transition function f(s,e), if the finite automaton is in state &#34;s 1  &#34; and the arithmetic/logic expression e evaluates to &#34;true&#34; for the present input symbol (row of the trace array), and f(s 1 ,e)=s 2 , then the finite automaton will go to state s 2 . 
     The arithmetic/logic expressions that are used with the finite automata according to the present invention are composed of fields, numbers, and arithmetic and logic operators. Fields are numbers that are constructed bitwise by extracting bits from an input symbol, which is a row of the trace array. The use of fields permits a single signal or the entire group of signals of a row to be tested or analyzed. Fields are shown subsequently in describing FIG. 7B. 
     The numbers and operators that are used in the arithmetic/logic expressions are according to those used in programming languages such as &#34;C.&#34; Numbers are unsigned integers that may be decimal, octal, hemidecimal, or binary. The arithmetic and logic operators may include those shown in Table 2. 
     
                       TABLE 2                                                     
______________________________________                                    
OPERATORS         FUNCTIONS                                               
______________________________________                                    
+                 addition                                                
-                 subtraction                                             
*                 multiplication                                          
/                 division                                                
%                 modulus                                                 
&amp;                 bit AND                                                 
|        bit inclusive OR                                        
                  bit exclusive OR                                        
˜           bit complement                                          
&amp;&amp;                logical AND                                             
||                                                      
                  logical inclusive OR                                    
!                 logical NOT                                             
&lt;&lt;                shift left                                              
&gt;&gt;                shift right                                             
&lt;                 less than                                               
&gt;                 greater than                                            
&lt;=                less than or equals                                     
&gt;=                greater than or equals                                  
==                equals                                                  
!=                not equals                                              
()                grouping                                                
______________________________________                                    
 
    
     The precedence for these operators when used in arithmetic/logic expressions is set forth in Table 3. 
     
                       TABLE 3                                                     
______________________________________                                    
Operator            Precedence                                            
______________________________________                                    
()                  Highest                                               
!,˜                                                                 
*,/,%                                                                     
+,-                                                                       
&lt;&lt;,&gt;&gt;                                                                     
&lt;,&lt;=,&gt;,&gt;=                                                                 
==,!=                                                                     
|                                                                
&amp;&amp;                                                                        
||                                                      
                    Lowest                                                
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     The arithmetic and logic operators operate the following preferred ways on their operands. The operators (+,-,*, /, %) treat their operands as unsigned integers and produce a result that is an unsigned integer. 
     The shift operators (&lt;&lt;,&gt;&gt;) treat their operands as unsigned integers and produce unsigned integers. Right shifting shifts &#34;0s&#34; into the most significant bit (MSB) of the result, and left shifting shifts &#34;0s&#34; into the least significant bit (LSB) of the result. 
     The comparison operators (&lt;,&gt;,&lt;=,&gt;=,!=) treat their operands as unsigned integers and produce a boolean result. That is, if the comparison is true, the value of the result is &#34;1&#34;, otherwise the value of the result is &#34;0.&#34; These operators always produce a value of &#34;1&#34; or &#34;0.&#34; 
     The bit operators (&amp;,|,,˜) treat their operands as bit fields and perform their operations bit-by-bit. 
     Logical operators (&amp;&amp;,||,!) treat their operands as booleans and produce a boolean result. If the operand is equal to &#34;0,&#34; it is taken as false, otherwise it is taken as true (&#34;1&#34;). If the result of the operation is logically false, the value of the result is &#34;0,&#34; otherwise the value of the result is &#34;1.&#34; These operators always produce a value of &#34;1&#34; or &#34;0.&#34; 
     For joining or dealing with more than one pattern, the arithmetic/logic expressions may be combined using the operators for concatenation, alternation, and repetition. These arithmetic/logic expressions when joined with the concatenation, alternation, and repetition operators form regular expressions according to the present invention. Following the present invention, the simplest form of a regular expression is a single arithmetic/logic expression. 
     In Table 4 below, the operator &#34;or&#34; is associated with alternation, the operator &#34;then&#34; is associated with concatenation, and the operator &#34;{ }&#34; is associated with repetition. The symbols a and b represent regular expressions. 
     
                       TABLE 4                                                     
______________________________________                                    
Concatenation   a then b                                                  
Alternation     a or b                                                    
Repetition      a{ }                                                      
______________________________________                                    
 
    
     Concatenation uses the operator &#34;then&#34; to join two patterns in series. In searching using concatenation, the system searches for the sequence of the two patterns. 
     Alternation is associated with the operator &#34;or.&#34; This joins two patterns in parallel and causes the system to search for a match of either of the two patterns. 
     The repetition is for determining the maximum and minimum number of a repeated pattern. 
     Referring to FIG. 7A and B, regular expressions that use &#34;then,&#34; &#34;or,&#34; and &#34;{ }&#34; operators, and arithmetic/logic expressions using fields, numbers, and arithmetic and logical operators will be discussed. In FIG. 7A, the partial traces for four of 64 signals that have been sampled 8 times are shown generally at 350. The signals are a, b, c, and d. As shown, the a signal is at 352, the b signal is at 354, the c signal is at 356, and the d signal is at 358. Since time progresses to the right in FIG. 7A, the trace can be partitioned vertically into slices as shown. 
     The state of signals a, b, c, and d in FIG. 7A also may be presented in a trace array as shown in FIG. 7B assuming that these signals are sampled at these times. FIG. 7B has representative rows 362, 364, 366, 368, 370, 372, 374, 376, and 378; and representative columns 380, 382, 384, 386, 388, and 390. 
     As shown, signals a, b, c, and d are single bit signals so fields representing these signals will also be of one bit. For example, the fields for these signals may be 
     
         field a 1,1(1) 
    
     
         field b 2,1(2) 
    
     
         field c 3,1(3) 
    
     
         field d 4,1(4) 
    
     where in field (x) (y,z): 
     x=Field name. 
     y=Leftmost bit of the field. 
     z=Bit length of the field. 
     As such, when signals that have a larger number of bits are considered, the desired field of these signals may be specified in this manner. 
     By way of example, possible regular expressions for finite automata that may be used to search a trace array for what is represented at time t 1 , t 2 , and t 8 , respectively, for the signals a, b, c, and d are the following: 
     
         ______________________________________                                    
At t.sub.1 :                                                              
  (a &amp;&amp; !b &amp;&amp; !c &amp;&amp; !d)                                                   
                   (5)                                                    
At t.sub.2 :                                                              
  (a &amp;&amp; b &amp;&amp; !c &amp;&amp; !d)                                                    
                   (6)                                                    
At t.sub.8 :                                                              
  (a &amp;&amp; b &amp;&amp; !c &amp;&amp; d)                                                     
                   (7)                                                    
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     It should be understood that these expressions would use the defined fields for the a, b, c, and d signals. 
     The operators &#34;then,&#34; &#34;or,&#34; and &#34;{ }&#34; are used to connect arithmetic/logic expressions to form regular expressions that are used in the finite automata according to the present invention. For example, suppose patterns of the a and b signals are of interest, in particular, at times t 1  and t 2 . A concatenation of the two arithmetic/logic expressions for use in searching is the following: 
     
         (a &amp;&amp; !b) then (a &amp;&amp; b)(8) 
    
     If the alternation operation is used instead of the concatenation operation, the expression would be the following: 
     
         (a &amp;&amp; !b) or (a &amp;&amp; d) (9) 
    
     Now if the desire is to search for situations in which there are a number of patterns like that at t 2  that follow a pattern like the one at t 1 , the expression is as follows: 
     
         ______________________________________                                    
((a &amp;&amp; !b &amp;&amp; !c) then                                                     
                  (10)                                                    
(a &amp;&amp; b &amp;&amp; !c) {3})                                                       
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     The finite automata evaluate the arithmetic/logic expressions to determine whether such expressions are zero with regard to a row or portion of a row of the large trace array. If an arithmetic/logic expression is zero, then the value is considered &#34;false&#34; and the finite automata does not enter that next state specified by the transition function. If, however, the arithmetic/logic expression is not a zero, then its value is considered &#34;true&#34; and the finite automata enters the next state specified by the transition function. 
     Referring to FIG. 8, the steps of the method of the present invention are shown generally at 400. According to the method, step 1 at 410 is where regular expressions that define the searches are input to the system capable of carrying out the search. At step 2 at 420, finite automata are generated which use arithmetic/logic expressions. Following step 2, there is step 3 at 430 where the large trace array that is input to the system capable of carrying out the search is read and searched with the finite automata which use arithmetic/logic expressions for desired patterns. And finally, at step 4 at 440, the results of the search are output from a system capable of carrying out the search. 
     FIG. 9 is a block diagram of the system of the present invention. The system is shown generally at 450. The first element of the system is regular expression input 451. The regular expressions that are used to define the search are input to the system here and fed to the next element of the system on line 452. 
     This next system element is generator 454. This generator is for generating finite automata which use arithmetic/logic expressions instead a particular symbol from a finite alphabet. The finite automata that are output from the generator are based on the regular expressions input to the system. 
     The finite automata that are output from generator 454 on line 456 are input to analyzer 460. The second input to the system is the large trace array that is input to analyzer 460 by way of trace array input 457 and input line 458. 
     The analyzer uses the finite automata to search the large trace array described above and the results of the search are output from analyzer 460 on line 462. It is understood that the generator and the analyzer may be configured as either special circuits or as a general purpose computer. 
     In accordance with the foregoing, the system and method of the present invention may be used for analyzing large trace arrays with finite automata using arithmetic/logic expressions. 
     Having now described searching using finite automata that use arithmetic/logic expressions in normal situations, the specification now will address situations when there are more complex sequences of events, such as when events overlap. An example of an overlapping situation is shown in FIG. 10. Although the use of multiple finite automata is described for analyzing large trace arrays with overlapping events, it is understood that multiple finite automata according to the present invention may be used for trace arrays of any size that have overlapping events, such as trace arrays of the size shown in FIG. 1 and trace arrays of the size of the ASCII text file shown in FIG. 5. 
     Again referring to FIG. 10, the cycles of a bus that includes the a signal is shown generally at 470. The bus is idle at the bus cycles shown at 471, 473, and 475, and is controlled by a device at 472 and 474. Specifically, at the bus cycle at 472, the bus is controlled by Device 0 and at 474, it is controlled by Device 1. 
     The request and grant timing diagrams for the Device 0 are shown at 479 and 480, respectively, and request and grant timing diagrams for the Device 1 are shown at 488 and 489, respectively. With regard to the timing diagrams for the Device 0, the Device 0 request line is inactive at 476, issues a request for the bus at 477, and again is inactive at 478. At grant signal timing diagram 480, the grant line is inactive at 481, becomes active at 483 in response to the request for the bus, and again becomes inactive at 484. The difference between the time the bus request is made and the time the request is granted is the latency for the Device 0. This latency is shown at 482. 
     The request and grant timing diagrams for the Device 1 is shown at 488 and 489, respectively. With regard to the request timing diagram, the Device 1 request line is inactive at 485 and active at 486 when it issues a request for the bus. It again becomes inactive at 487. The grant timing diagram at 489 shows that the grant line is inactive at 491 and active at 490 when the Device 1 is granted the bus. The grant line returns to an inactive state at 493. 
     With regard to the Device 1 latency, the Device 0 was granted the bus during bus cycle 472, based on a request that was shortly before the request by the Device 1. The grant 1 must wait until bus cycle 473 before the bus request 1 is granted. Accordingly, the latency for the Device 1 is at 492. This second latency is longer than that for the Device 0. 
     If it is desired to know where the positions of the idle and active periods are of the bus cycles, this could be done by writing a pattern to obtain the information. Given the bus cycles at 470, a pattern could be easily written. It may also be desirable to determine what device created a bus cycle. A single finite automaton could be used for this purpose as long as there is no overlap. 
     When there is overlap as shown for the latencies of the two devices, a single finite automaton at certain instances may obtain a latency reading which would not distinguish which latency had been found. For example, suppose that there is a latency problem and that latency problem is associated with the Device 1. As shown in FIG. 10, there are two latencies: one associated with the Device 0 and one associated with Device 1. If a search is generated using a single finite automaton, that search would fail to correctly identify both latencies. For example, a search using a single finite automaton would identify the latency at 482 or at 492, but not both. In order to eliminate the overlapping problem, separate finite automata are used to search the latency conditions for the Device 0 and the Device 1. 
     The method that the present invention uses to solve the problem of complex overlapping sequences of events is to analyze trace arrays using multiple finite automata with cross communications. By this method, each finite automaton analyzes the trace array to produce its own series of non-overlapping tokens. 
     For example, a data bus that is part of a large trace array might be analyzed by a combination of three finite automata. In this situation, one finite automaton partitions the events for the data signals, a second finite automaton partitions the events for the arbitration signals, and a third finite automaton partitions the entire trace array by examining the event partitions produced by the first and second finite automata. To do this, it is necessary for the first and second finite automata to communicate with the third finite automaton. Moreover, it also may be necessary for the third finite automaton to communicate back to the first and second finite automata to influence their partitioning of the data and arbitration signals. 
     According to this aspect of the present invention, patterns to be searched are specified in regular expressions; however, instead of the regular expressions being converted to a single finite automaton which uses arithmetic/logic expressions, the regular expressions are grouped and each group is then converted to a separate finite automaton based on the groupings to form multiple finite automata which use arithmetic/logic expressions. When a search of a trace array takes place, each finite automaton of the multiple automata separately searches the array. These separate searches are conducted in parallel. 
     According to the present invention, communications between the respective finite automata are facilitated by augmenting the trace array with additional columns as shown in FIG. 11. In FIG. 11, a 64 signal by 2,097,152 sample trace array is shown at 495. The additional columns for communications use are shown at 496, 497, and 498. When one of the finite automata finds a pattern that it has been searching for, it may write to these extra columns which are shown as columns 65, 66, 67 in FIG. 11. These extra columns expand the character set used by the finite automata. However, since the finite automata use arithmetic/logic expressions which embrace the use of an infinite alphabet, it is easy to include these columns in the character set. 
     Since these columns may be considered part of the character set, they also may be part of regular expressions that form other finite automata. As such, these other finite automata may effectively read the data in the extra columns which were written to by a first finite automaton. This, therefore, results in communications among the multiple finite automata. 
     In FIG. 12, the steps of the method of the present invention for handling complex overlapping sequences requiring the use of multiple finite automata is shown generally at 500. According to this method, step 1 at 510 is where the regular expressions grouped in a predetermined way are input to an apparatus capable of performing the search. Step 2 at 520 is where the multiple finite automata are generated according the earlier groupings of regular expressions. Each finite automaton that is generated uses arithmetic/logic expressions which permits the use of an infinite alphabet. At step 3 at 530, the trace array is read and searched by the multiple finite automata in parallel. At this step, any of the finite automata that find a pattern may write to the extra columns of the trace array so that other finite automata that read the extra columns may identify such data. Step 4 at 540 is where the results of the search are output from a system capable of carrying out the search. 
     FIG. 13 is a block diagram of the system of the present invention when multiple automata with cross communications are used. The system of this aspect of the present invention is shown generally at 550. The first element of system 550 is input 551 where regular expressions that are grouped according to the finite automata they are to generate are input to the system. Input 551 connects to line 552. 
     The next system element is generator 554. This generator is for generating a separate finite automaton according to each grouping of regular expressions. Each finite automaton of the multiple finite automata which are generated use arithmetic/logic expressions. The multiple finite automata that are generated at generator 554 are output on line 556. Line 556 connects to the input of analyzer 560. 
     The second input to system 550 is the trace array that is input to analyzer 560 by way of trace array input 557 and input line 558. The analyzer uses each of the multiple finite automata to search the large trace array. The separate searches are carried out in parallel. During the search, the analyzer may use the extra columns of the trace array (see FIG. 11) for communications among the finite automata. The search results are output from analyzer 560 on line 562. It is understood that the generator and the analyzer may be configured as either special circuits or as a general purpose computer. 
     The terms and expressions which are employed herein are used as terms of expression and not of limitation. And, there is no intention, in the use of such terms and expressions, of excluding the equivalents of the features shown, and described, or portions thereof, it being recognized that various modifications are possible within the scope of the invention.