Abstract:
An apparatus and method for transmitting information between dual redundant components comprises two information sources each of which is coupled to two transmitters, the outputs of which are coupled to four signal paths for transmission to two independent voters. Each of the voters compares predetermined pairs of the signals on the four signal paths and provides a preferred one of the signals to a corresponding receiver based on the results of the pair comparisons.

Description:
BACKGROUND OF THE INVENTION 
     This invention relates in general to the transmission of redundant information over multiple communication paths and more particularly to a method and apparatus for communication of dual redundant information over four communication paths, wherein comparisons are made of certain path pairs in order to provide an indication of the goodness or failure of the signal on a given path. 
     One of the common current methods of utilizing four signal paths to transmit information between dual redundant components is to simply use the paths as two separate pairs. The common method of detecting a failure using this method is to simply compare the information on one of the paths of a given pair with that on the other path of that same pair. If there is disagreement, that pair is determined to be unusable. Both pairs are similarly checked. Reception succeeds if either pair has information from its two paths that agree. While this method does accomplish accurate failure detection and appropriate identification of the remaining valid information source, there are other pair comparisons which could be made and utilized to identify other valid information source combinations. 
     SUMMARY OF THE INVENTION 
     In order to accomplish additional valid information comparisons, the output from a first information source is input to first and second transmitters, the outputs of which are coupled to first and second paths for transmission of the information to first and second voters. The output information from a second information source is coupled to the inputs of third and fourth transmitters, the outputs of which are coupled to third and fourth paths for transmission of the information to first and second voters. The outputs of the first, second, third and fourth transmitters are compared by the first and second voters in a predetermined manner to determine which of the signals on the four paths compare. If one or more do not compare with the remaining signals, the voter selects appropriate information to be transferred to a first receiver and the second voter selects appropriate information to be provided to a second receiver. 
     The comparisons accomplished in the first and second voters involve comparisons of the information on the first and third paths, the second and fourth paths, the first and fourth paths, and the information on the second and third paths, but not the information on the first and second, or third and fourth paths. Using these various pair combinations, a logic decision is made to determine which of the signals on the paths are acceptable for use by the first and second receivers. In addition, the first and second voters may provide comparison between themselves to confirm that each has made the same selection of the information to be used by the receivers. 
     In an additional feature, apparatus may be included to detect the loss of transmission of information on each of the four paths. This loss of transmission information is combined with the comparison information to provide a logic decision to determine which of the signals are acceptable for use by the receivers and to indicate the degree of confidence in each signal. 
     The features and advantages of the present invention will become apparent upon consideration of the following description of the preferred embodiments of the present invention when taken in conjunction with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram illustrating the components of the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The apparatus of the present invention as shown in FIG. 1 is a configuration where data from one dual device, comprising information sources 10 and 20, is used to transmit data over four separate signal lines 35, 45, 65 and 75 via transmitters 30, 40, 60, and 70 respectively, to two independent voters 50 and 80. These voters evaluate the signals Ax, Bx, Ay and By on the four signal lines 35, 45, 65, and 75 and provide a single signal source via outputs 52 and 82 to dual information receivers 90 and 100. Voter blocks 50 and 80 each compare lines 35 to 65, 45 to 75, 35 to 75 and 45 to 65. This produces a four bit syndrome (one bit for each comparison) which is used to select an error free signal for the set (35, 65, 45, 75) or, if no error free signal can be determined, an &#34;uncorrectable error&#34; condition is indicated. 
     The truth table for the four bit syndrome is shown in Table 1 and indicates the logic decision accomplished for output by each of the independent voters based on the truth of the pair comparisons of the four signals in the four combinations indicated. Since each of the independent voters 50 and 80 performs the identical comparison, the resultant signal applied to receiver 90 and receiver 100 should be identical, in most cases. 
     The logic decisions made by the separate voters may be compared via lines 58 and 88 to insure that the same signal is in fact selected for the separate independent receivers. Alternative methods of comparing the voter decisions are possible. An exchange of validity signals between voters can be used, with each voter then selecting any signal which falls into the intersection of the sets of validity decisions of both voters. These validity signals can either be the syndrome set or the set identifying valid signals. Alternatively, the voters may simply exchange all of the data signals, as received, with each other and perform any of several well known comparison methods of selecting a valid signal from the resultant eight data signals which should be identical. 
     This comparison between voters detects faults in the receiver and voter functions of the voters. This comparison also detects those rare faults in the transmitters or the signal lines which cause a signal from a single signal line to appear simultaneously to have different values as perceived by the two voters. This is known in the art as the Byzantine Generals&#39; problem. 
     The signals on lines 35, 45, 65, and 75 are respectively labeled as signals Ax, Bx, Ay and By in Tables 1, 2, and 3. As indicated in Table 1, the additional comparisons of Ax to By and Bx to Ay provide additional success sets which will allow for operation under conditions which would not be accomplished using the standard prior art comparison involving only Ax to Bx, or Ay to By. 
     As shown in Table 1, where three or more of the four comparisons made are true, a decision can be made to elect the use of a signal output with relative certainty as to its validity. These decisions are shown in the &#34;Integrity&#34; column of Table 1. In those cases where only one or two of the four comparisons are true, a decision may be made to utilize a signal which had one or two correct comparisons, but with less confidence than when three or more of the four comparisons were true. These decisions are shown in the &#34;Availability&#34; column of Table 1. 
     In this manner, a user of the received signal may elect to use a given signal in a different manner based on the output of the comparison made, depending on the critical nature of the signal in question. For example, in the case of a flight control signal, a very high confidence level would be desired, whereas less critical signals, such as a navigation related information, may be used with a decreased confidence level and an annunciation indicating a decreased confidence level. Those systems which use binary confidence levels (e.g., good and bad) can convert the decreased confidence level to high or low confidence depending on whether the signal in question is of high or low criticality. 
     In addition to the comparison function, each of the voters 50 and 80 may receive an additional logic signal from a separate apparatus 54, 84 which detects the loss of transmission of any signal on each of the four signal paths. This separate logic information, shown in the &#34;Quanta Received&#34; column of Tables 2.1-2.6 and 3.1-3.6, may be combined with the previously described comparison information to provide additional sets of logic decisions which indicate both possible failures and the relative confidence of the remaining signals. 
     Those combinations of comparison information and received signal information resulting in relatively high confidence are shown in Tables 2.1-2.6 in the columns labeled &#34;Integrity&#34;. A &#34;Y&#34; in the Ax, Ay, Bx or By &#34;Quanta Valid&#34; columns of Table 2 indicates that particular signal (Ax, Ay, Bx or By) may be used with a relatively high confidence level for the given comparison syndrome and quanta received failures indicated. 
     Those combinations of comparison information and received signal information resulting in a lower degree of confidence, but still some probability of useful information, are shown in the column of Tables 3.1-3.6 labeled &#34;Availability&#34;. A &#34;Y&#34; with an asterisk indicates the particular signals (Ax, Ay, Bx or By) which may by used with a lower degree of confidence, but still a relatively high probability of obtaining useful information. The remaining signal information identified with a &#34;Y&#34; in the &#34;Availability&#34; column of Tables 3.1-3.6 is identical to that from the higher confidence level &#34;Integrity&#34; column of Tables 2.1-2.6 and is repeated in Tables 3.1-3.6 for comparison. 
     The described logic and comparison functions may be implemented using any of a number of electronic devices capable of performing the described functions, or preferably in an Application Specific Integrated Circuit (ASIC) designed for the specific described functions. 
     While the invention has been described in conjunction with a particular apparatus and implementation, other equivalent implementations may be made without departing from scope of the invention. 
     
                                           TABLE 1__________________________________________________________________________Syndrome            VALID SIGNALS                          VALID SIGNALSAx=AyBx=By     Ax=By          Bx=Ay               (Safety)   (Availability)__________________________________________________________________________T    T    T    T    Any bus    Any busT    T    T    F    Ax or By   Ax or ByT    T    F    T    Bx or Ay   Bx or AyT    T    F    F    Uncorrectable Error                          Any bus__________________________________________________________________________T    F    T    T    Ax orAy    Ax or AyT    F    T    F    Uncorrectable Error                          AxT    F    F    T    Uncorrectable Error                          AyT    F    F    F    Uncorrectable Error                          Ax or Ay__________________________________________________________________________F    T    T    T    Bx or By   Bx or ByF    T    T    F    Uncorrectable Error                          ByF    T    F    T    Uncorrectable Error                          BxF    T    F    F    Uncorrectalbe Error                          Bx or By__________________________________________________________________________F    F    T    T    Uncorrectable Error                          Any busF    F    T    F    Uncorrectable Error                          Ax or ByF    F    F    T    Uncorrectable Error                          Bx or AyF    F    F    F    Uncorrectable Error                          Uncorrectable Error__________________________________________________________________________ 
    
     
                                           TABLE 2.1__________________________________________________________________________                       IntegrityQuanta Received    Syndrome           Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T T T T  T    T    T    T    Y Y Y Y All matchT T T T  T    T    T    F    Y     Y Checker failure; distrust Ax &amp; BxT T T T  T    T    F    T      Y Y   Checker failure; distrust Ax &amp; ByT T T T  T    T    F    F            2-2 tie Ax=Ay; Bx=ByT T T T  T    F    T    T    Y Y     Checker failure; distrust Bx &amp; ByT T T T  T    F    T    F    Y Y   Y Bx badT T T T  T    F    F    T    Y Y Y   By badT T T T  T    F    F    F            Dual non-identical failure on BxByT T T T  F    T    T    T        Y Y Checker failure; distrust Ax &amp; AyT T T T  F    T    T    F    Y   Y Y Ay badT T T T  F    T    F    T      Y Y Y Ax badT T T T  F    T    F    F            Dual non-identical failure on AxAyT T T T  F    F    T    T            2-2 tie Ax=By; Bx=AyT T T T  F    F    T    F            Dual non-identical failure on BxAyT T T T  F    F    F    T            Dual non-identical failure on AxByT T T T  F    F    F    F            Nothing matches - triple__________________________________________________________________________                                failure                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F T T T  T    T    T    T      Y Y Y All match but Ax missingF T T T  T    T    T    F            Checker failure; can&#39;t isolateF T T T  T    T    F    T      Y Y   Checker failure; distrust Ax &amp; ByF T T T  T    T    F    F        Y Y Bx=By; Ax msng; transient on AyF T T T  T    F    T    T            Checker failure; can&#39;t isolateF T T T  T    F    T    F            Ax msng &amp; Bx bad =&gt; UncorrectableF T T T  T    F    F    T      Y Y   By bad &amp; Ax msngF T T T  T    F    F    F            Dual non-identical failure on BxByF T T T  F    T    T    T        Y Y Checker failure; distrust Ax &amp; AyF T T T  F    T    T    F        Y Y Ay bad &amp; Ax missingF T T T  F    T    F    T      Y Y Y Ax bad (normal syndrome for Ax                                msng)F T T T  F    T    F    F        Y Y Bx=Ay; Ax msng; transient on ByF T T T  F    F    T    T      Y Y   Bx=Ay; Ax msng; transient on ByF T T T  F    F    T    F            Dual non-identical failure on BxAyF T T T  F    F    F    T      Y Y   Bx=Ay; Ax msng; transient on ByF T T T  F    F    F    F            Nothing matches - triple__________________________________________________________________________                                failure                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T F T T  T    T    T    T    Y   Y Y All match but Ay missingT F T T  T    T    T    F    Y     Y Checker failure distrust Ay &amp; BxT F T T  T    T    F    T            Checker failure; can&#39;t isolateT F T T  T    T    F    F        Y Y Bx=By; Ay msng; transient on AxT F T T  T    F    T    T            Checker failure; can&#39;t isolateT F T T  T    F    T    F    Y     Y Bx bad &amp; Ay missingT F T T  T    F    F    T            Ay msng &amp; By bad =&gt; UncorrectableT F T T  T    F    F    F            Dual non-identical failure on BxByT F T T  F    T    T    T        Y Y Checker failure; distrust Ax &amp; AyT F T T  F    T    T    F    Y   Y Y Ay bad (normal syndrome for Ay                                msng)T F T T  F    T    F    T        Y Y Ax bad &amp; Ay missingT F T T  F    T    F    F        Y Y Bx=By; Ay msng; transient on AxT F T T  F    F    T    T    Y     Y Ax=By; Ay msng; transient on BxT F T T  F    F    T    F    Y     Y Ax=By; Ay msng; transient on BxT F T T  F    F    F    T            Dual non-identical failure on AxByT F T T  F    F    F    F            Nothing matches - triple__________________________________________________________________________                                failure 
    
     
                                           TABLE 2.2__________________________________________________________________________                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T T F T  T    T    T    T    Y Y   Y All match but Bx missingT T F T  T    T    T    F    Y     Y Checker failure; distrust Ay &amp; BxT T F T  T    T    F    T            Checker failure; can&#39;t isolateT T F T  T    T    F    F    Y Y     Ax=Ay; Bx msng; transient on ByT T F T  T    F    T    T    Y Y     Checker failure; distrust Bx &amp; ByT T F T  T    F    T    F    Y Y   Y Bx bad (normal syndrome for Bx msngT T F T  T    F    F    T    Y Y     By bad &amp; Bx missingT T F T  T    F    F    F    Y Y     Ax=Ay; Bx msng; transient on ByT T F T  F    T    T    T            Checker failure; can&#39;t isolateT T F T  F    T    T    F    Y     Y Ay bad &amp; Bx missingT T F T  F    T    F    T            Bx msng &amp; Ax bad =&gt; UncorrectableT T F T  F    T    F    F            Dual non-identical failure on AxAyT T F T  F    F    T    T    Y     Y Ax=By; Bx msng; transient on AyT T F T  F    F    T    F    Y     Y Ax=By; Bx msng; transient on AyT T F T  F    F    F    T            Dual non-identical failure on AxByT T F T  F    F    F    F            Nothing matches - triple__________________________________________________________________________                                failure                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T T T F  T    T    T    T    Y Y Y   All match but By missingT T T F  T    T    T    F            Checker failure; can&#39;t isolateT T T F  T    T    F    T      Y Y   Checker failure; distrust Ax &amp; ByT T T F  T    T    F    F    Y Y     Ax=Ay; By msng; transient on BxT T T F  T    F    T    T    Y Y     Checker failure; distrust Bx &amp; ByT T T F  T    F    T    F    Y Y     Bx bad &amp; By missingT T T F  T    F    F    T    Y Y Y   By bad (normal syndrome for By                                msng)T T T F  T    F    F    F    Y Y     Ax=Ay; By msng; transient on BxT T T F  F    T    T    T            Checker failure; can&#39;t isolateT T T F  F    T    T    F            By msng &amp; Ay bad =&gt; UncorrectableT T T F  F    T    F    T      Y Y   Ax bad &amp; By missingT T T F  F    T    F    F            Dual non-identical failure on AxAyT T T F  F    F    T    T      Y Y   Bx=Ay; By msng; transient on AxT T T F  F    F    T    F            Dual non-identical failure on BxAyT T T F  F    F    F    T      Y Y   Bx=Ay; By msng; transient on AxT T T F  F    F    F    F            Nothing matches - triple__________________________________________________________________________                                failure                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F F T T  T    T    T    T        Y Y Ax &amp; Ay msng: Bx=ByF F T T  T    T    T    F        Y Y Ax &amp; Ay msng: Bx=ByF F T T  T    T    F    T        Y Y Ax &amp; Ay msng: Bx=ByF F T T  T    T    F    F        Y Y Ax &amp; Ay msng: Bx=ByF F T T  T    F    T    T            Ax &amp; Ay msng: Bx≠By =&gt;                                UncorrectableF F T T  T    F    T    F            Ax &amp; Ay msng: Bx≠By =&gt;                                UncorrectableF F T T  T    F    F    T            Ax &amp; Ay msng: Bx≠By =&gt;                                UncorrectableF F T T  T    F    F    F            Ax &amp; Ay msng: Bx≠By =&gt;                                UncorrectableF F T T  F    T    T    T        Y Y Ax &amp; Ay msng: Bx=ByF F T T  F    T    T    F        Y Y Ax &amp; Ay msng: Bx=ByF F T T  F    T    F    T        Y Y Ax &amp; Ay msng: Bx=ByF F T T  F    T    F    F        Y Y Ax &amp; Ay msng: Bx=ByF F T T  F    F    T    T            Ax &amp; Ay msng: Bx≠By =&gt;                                UncorrectableF F T T  F    F    T    F            Ax &amp; Ay msng: Bx≠By =&gt;                                UncorrectableF F T T  F    F    F    T            Ax &amp; Ay msng: Bx≠By =&gt;                                UncorrectableF F T T  F    F    F    F            Ax &amp; Ay msng: Bx≠By =&gt;                                Uncorrectable__________________________________________________________________________ 
    
     
                                           TABLE 2.3__________________________________________________________________________                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T T F F  T    T    T    T    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    T    T    F    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    T    F    T    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    T    F    F    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    F    T    T    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    F    T    F    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    F    F    T    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    F    F    F    Y Y     Bx &amp; By msng; Ax=AyT T F F  F    T    T    T            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    T    T    F            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    T    F    T            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    T    F    F            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    F    T    T            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    F    T    F            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    F    F    T            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    F    F    F            Bx &amp; By msng; Ax≠Ay =&gt;                                Uncorrectable__________________________________________________________________________                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                    Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F T T F  T    T    T    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  T    T    T    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  T    T    F    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  T    T    F    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  T    F    T    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  T    F    T    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  T    F    F    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  T    F    F    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  F    T    T    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  F    T    T    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  F    T    F    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  F    T    F    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  F    F    T    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  F    F    T    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  F    F    F    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  F    F    F    F            Ax &amp; By msng; Bx≠Ay =&gt;                                Uncorrectable__________________________________________________________________________                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T F F T  T    T    T    T    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  T    T    T    F    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  T    T    F    T            Bx &amp; Ay msng: Ax≠By =&gt;                                UncorrectableT F F T  T    T    F    F            Bx &amp; Ay msng: Ax≠By ≠&gt;                                UncorrectableT F F T  T    F    T    T    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  T    F    T    F    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  T    F    F    T            Bx &amp; Ay msng: Ax≠By =&gt;                                UncorrectableT F F T  T    F    F    F            Bx &amp; Ay msng: Ax≠By =&gt;                                UncorrectableT F F T  F    T    T    T    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  F    T    T    F    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  F    T    F    T            Bx &amp; Ay msng: Ax≠By =&gt;                                UncorrectableT F F T  F    T    F    F            Bx &amp; Ay msng: Ax≠By =&gt;                                UncorrectableT F F T  F    F    T    T    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  F    F    T    F    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  F    F    F    T            Bx &amp; Ay msng: Ax≠By =&gt;                                UncorrectableT F F T  F    F    F    F            Bx &amp; Ay msng: Ax≠By =&gt;                                Uncorrectable__________________________________________________________________________ 
    
     
                                           TABLE 2.4__________________________________________________________________________                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F T F T  T    T    T    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    T    T    F    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    T    F    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    T    F    F    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    F    T    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    F    T    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    F    T    F    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    F    F    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    T    T    T        X X Both Ax and Bx msng; No quanta cmprF T F T  F    T    T    F    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    T    F    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    T    F    F    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    F    T    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    F    T    F    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    F    F    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    F    F    F    X X X X Both Ax and Bx msng; No quanta__________________________________________________________________________                                cmpr                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T F T F  T    T    T    T    X X X X Both Ay and By msng; No quanta cmprT F T F  T    T    T    F    X X X X Both Ay and By msng; No quanta cmprT F T F  T    T    F    T    X X X X Both Ay and By msng; No quanta cmprT F T F  T    T    F    F    X X X X Both Ay and By msng; No quanta cmprT F T F  T    F    T    T    X X X X Both Ay and By msng; No quanta cmprT F T F  T    F    T    F    X X X X Both Ay and By msng; No quanta cmprT F T F  T    F    F    T    X X X X Both Ay and By msng; No quanta cmprT F T F  T    F    F    F    X X X X Both Ay and By msng; No quanta cmprT F T F  F    T    T    T    X X X X Both Ay and By msng; No quanta cmprT F T F  F    T    T    F    X X X X Both Ay and By msng; No quanta cmprT F T F  F    T    F    T    X X X X Both Ay and By msng; No quanta cmprT F T F  F    T    F    F    X X X X Both Ay and By msng; No quanta cmprT F T F  F    F    T    T    X X X X Both Ay and By msng; No quanta cmprT F T F  F    F    T    F    X X X X Both Ay and By msng; No quanta cmprT F T F  F    F    F    T    X X X X Both Ay and By msng; No quanta cmprT F T F  F    F    F    F    X X X X Both Ay and By msng; No quanta__________________________________________________________________________                                cmpr                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T F F F  T    T    T    T    X X X X Three busses msng; No quanta comprT F F F  T    T    T    F    X X X X Three busses msng; No quanta comprT F F F  T    T    F    T    X X X X Three busses msng; No quanta comprT F F F  T    T    F    F    X X X X Three busses msng; No quanta comprT F F F  T    F    T    T    X X X X Three busses msng; No quanta comprT F F F  T    F    T    F    X X X X Three busses msng; No quanta comprT F F F  T    F    F    T    X X X X Three busses msng; No quanta comprT F F F  T    F    F    F    X X X X Three busses msng; No quanta comprT F F F  F    T    T    T    X X X X Three busses msng; No quanta comprT F F F  F    T    T    F    X X X X Three busses msng; No quanta comprT F F F  F    T    F    T    X X X X Three busses msng; No quanta comprT F F F  F    T    F    F    X X X X Three busses msng; No quanta comprT F F F  F    F    T    T    X X X X Three busses msng; No quanta comprT F F F  F    F    T    F    X X X X Three busses msng; No quanta comprT F F F  F    F    F    T    X X X X Three busses msng; No quanta comprT F F F  F    F    F    F    X X X X Three busses msng; No quanta__________________________________________________________________________                                compr 
    
     
                                           TABLE 2.5__________________________________________________________________________                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F T F F  T    T    T    T    X X X X Three busses msng; No quanta comprF T F F  T    T    T    F    X X X X Three busses msng; No quanta comprF T F F  T    T    F    T    X X X X Three busses msng; No quanta comprF T F F  T    T    F    F    X X X X Three busses msng; No quanta comprF T F F  T    F    T    T    X X X X Three busses msng; No quanta comprF T F F  T    F    T    F    X X X X Three busses msng; No quanta comprF T F F  T    F    F    T    X X X X Three busses msng; No quanta comprF T F F  T    F    F    F    X X X X Three busses msng; No quanta comprF T F F  F    T    T    T    X X X X Three busses msng; No quanta comprF T F F  F    T    T    F    X X X X Three busses msng; No quanta comprF T F F  F    T    F    T    X X X X Three busses msng; No quanta comprF T F F  F    T    F    F    X X X X Three busses msng; No quanta comprF T F F  F    F    T    T    X X X X Three busses msng; No quanta comprF T F F  F    F    T    F    X X X X Three busses msng; No quanta comprF T F F  F    F    F    T    X X X X Three busses msng; No quanta comprF T F F  F    F    F    F    X X X X Three busses msng; No quanta__________________________________________________________________________                                compr                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F F T F  T    T    T    F    X X X X Three busses msng; No quanta comprF F T F  T    T    T    F    X X X X Three busses msng; No quanta comprF F T F  T    T    F    T    X X X X Three busses msng; No quanta comprF F T F  T    T    F    F    X X X X Three busses msng; No quanta comprF F T F  T    F    T    T    X X X X Three busses msng; No quanta comprF F T F  T    F    T    F    X X X X Three busses msng; No quanta comprF F T F  T    F    F    T    X X X X Three busses msng; No quanta comprF F T F  T    F    F    F    X X X X Three busses msng; No quanta comprF F T F  F    T    T    T    X X X X Three busses msng; No quanta comprF F T F  F    T    T    F    X X X X Three busses msng; No quanta comprF F T F  F    T    F    T    X X X X Three busses msng; No quanta comprF F T F  F    T    F    F    X X X X Three busses msng; No quanta comprF F T F  F    F    T    T    X X X X Three busses msng; No quanta comprF F T F  F    F    T    F    X X X X Three busses msng; No quanta comprF F T F  F    F    F    T    X X X X Three busses msng; No quanta comprF F T F  F    F    F    F    X X X X Three busses msng; No quanta__________________________________________________________________________                                compr                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F F F T  T    T    T    F    X X X X Three busses msng; No quanta comprF F F T  T    T    T    F    X X X X Three busses msng; No quanta comprF F F T  T    T    F    T    X X X X Three busses msng; No quanta comprF F F T  T    T    F    F    X X X X Three busses msng; No quanta comprF F F T  T    F    T    T    X X X X Three busses msng; No quanta comprF F F T  T    F    T    F    X X X X Three busses msng; No quanta comprF F F T  T    F    F    T    X X X X Three busses msng; No quanta comprF F F T  T    F    F    F    X X X X Three busses msng; No quanta comprF F F T  F    T    T    T    X X X X Three busses msng; No quanta comprF F F T  F    T    T    F    X X X X Three busses msng; No quanta comprF F F T  F    T    F    T    X X X X Three busses msng; No quanta comprF F F T  F    T    F    F    X X X X Three busses msng; No quanta comprF F F T  F    F    T    T    X X X X Three busses msng; No quanta comprF F F T  F    F    T    F    X X X X Three busses msng; No quanta comprF F F T  F    F    F    T    X X X X Three busses msng; No quanta comprF F F T  F    F    F    F    X X X X Three busses msng; No quanta__________________________________________________________________________                                compr 
    
     
                                           TABLE 2.6__________________________________________________________________________                        IntegrityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F F F F  T    T    T    T    X X X X All busses msng; No quanta comprF F F F  T    T    T    F    X X X X All busses msng; No quanta comprF F F F  T    T    F    T    X X X X All busses msng; No quanta comprF F F F  T    T    F    F    X X X X All busses msng; No quanta comprF F F F  T    F    T    T    X X X X All busses msng; No quanta comprF F F F  T    F    T    F    X X X X All busses msng; No quanta comprF F F F  T    F    F    T    X X X X All busses msng; No quanta comprF F F F  T    F    F    F    X X X X All busses msng; No quanta comprF F F F  F    T    T    T    X X X X All busses msng; No quanta comprF F F F  F    T    T    F    X X X X All busses msng; No quanta comprF F F F  F    T    F    T    X X X X All busses msng; No quanta comprF F F F  F    T    F    F    X X X X All busses msng; No quanta comprF F F F  F    F    T    T    X X X X All busses msng; No quanta comprF F F F  F    F    T    F    X X X X All busses msng; No quanta comprF F F F  F    F    F    T    X X X X All busses msng; No quanta comprF F F F  F    F    F    F    X X X X All busses msng; No quanta__________________________________________________________________________                                compr 
    
     
                                           TABLE 3.1__________________________________________________________________________                       AvailabilityQuanta Received    Syndrome           Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T T T T  T    T    T    T    Y Y Y Y All matchT T T T  T    T    T    F    Y Y*                            Y*                              Y Checker failure; data is fineT T T T  T    T    F    T    Y*                          Y Y Y*                                Checker failure; data is fineT T T T  T    T    F    F    Y*                          Y*                            Y*                              Y*                                2-2 tie Ax=Ay; Bx=By; pick oneT T T T  T    F    T    T    Y Y Y*                              Y*                                Checker failure; data is fineT T T T  T    F    T    F    Y Y   Y Bx badT T T T  T    F    F    T    Y Y Y   By badT T T T  T    F    F    F    Y*                          Y*    Dual non-identical failure on BxByT T T T  F    T    T    T    Y*                          Y*                            Y Y Checker failure; data is fineT T T T  F    T    T    F    Y   Y Y Ay badT T T T  F    T    F    T      Y Y Y Ax badT T T T  F    T    F    F        Y*                              Y*                                Dual non-identical failure on AxAyT T T T  F    F    T    T    Y*                          Y*                            Y*                              Y*                                2-2 tie Ax=By; Bx=Ay; pick oneT T T T  F    F    T    F    Y*    Y*                                Dual non-identical failure on BxAyT T T T  F    F    F    T      Y*                            Y*  Dual non-identical failure on AxByT T T T  F    F    F    F            Nothing matches - triple__________________________________________________________________________                                failure                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F T T T  T    T    T    T      Y Y Y All match but Ax missingF T T T  T    T    T    F        Y*                              Y*                                Checker failure; distrust AyF T T T  T    T    F    T      Y Y Y*                                Checker failure; data is fineF T T T  T    T    F    F        Y Y Bx=By; Ax msng; transient on AyF T T T  T    F    T    T      Y*                            Y*  Checker failure; distrust ByF T T T  T    F    T    F            Ax msng &amp; Bx bad =&gt; UncorrectableF T T T  T    F    F    T      Y Y   By bad &amp; Ax msngF T T T  T    F    F    F            Dual non-identical failure on BxByF T T T  F    T    T    T      Y*                            Y Y Checker failure; data is fineF T T T  F    T    T    F        Y Y Ay bad &amp; Ax missingF T T T  F    T    F    T      Y Y Y Ax bad (normal syndrome for Ax                                msng)F T T T  F    T    F    F        Y Y Bx=Ay; Ax msng; transient on AyF T T T  F    F    T    T      Y Y   Bx=Ay; Ax msng; transient on ByF T T T  F    F    T    F            Dual non-identical failure on BxAyF T T T  F    F    F    T      Y Y   Bx=Ay; Ax msng; transient on ByF T T T  F    F    F    F            Nothing matches - triple__________________________________________________________________________                                failure                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T F T T  T    T    T    T    Y   Y Y All match but Ay missingT F T T  T    T    T    F    Y   Y*                              Y Checker failure; data is fineT F T T  T    T    F    T        Y*                              Y*                                Checker failure; distrust AxT F T T  T    T    F    F        Y Y Bx=By; Ay msng; transient on AxT F T T  T    F    T    T    Y*    Y*                                Checker failure; distrust BxT F T T  T    F    T    F    Y     Y Bx bad &amp; Ay missingT F T T  T    F    F    T            Ay msng &amp; By bad =&gt; UncorrectableT F T T  T    F    F    F            Dual non-identical failure on BxByT F T T  F    T    T    T    Y*  Y Y Checker failure; data is fineT F T T  F    T    T    F    Y   Y Y Ay bad (normal syndrome for Ay                                msng)T F T T  F    T    F    T        Y Y Ax bad &amp; Ay missingT F T T  F    T    F    F        Y Y Bx=By; Ay msng; transient on AxT F T T  F    F    T    T    Y     Y Ax=By; Ay msng; transient on BxT F T T  F    F    T    F    Y     Y Ax=By; Ay msng; transient on BxT F T T  F    F    F    T            Dual non-identical failure on AxByT F T T  F    F    F    F            Nothing matches - triple__________________________________________________________________________                                failure *Entry which is different between Integrity and Availability 
    
     
                                           TABLE 3.2__________________________________________________________________________                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T T F T  T    T    T    T    Y Y   Y All match but Bx missingT T F T  T    T    T    F    Y Y*  Y Checker failure; data is fineT T F T  T    T    F    T    Y*                          Y*    Checker failure; distrust ByT T F T  T    T    F    F    Y Y     Ax=Ay; Bx msng; transient on ByT T F T  T    F    T    T    Y Y   Y*                                Checker failure; data is fineT T F T  T    F    T    F    Y Y   Y Bx bad (normal syndrome for Bx msngT T F T  T    F    F    T    Y Y     By bad &amp; Bx missingT T F T  T    F    F    F    Y Y     Ax=Ay; Bx msng; transient on ByT T F T  F    T    T    T    Y*    Y*                                Checker failure; distrust AyT T F T  F    T    T    F    Y     Y Ay bad &amp; Bx missingT T F T  F    T    F    T            Bx msng &amp; Ax bad =&gt; UncorrectableT T F T  F    T    F    F            Dual non-identical failure on AxAyT T F T  F    F    T    T    Y     Y Ax=By; Bx msng; transient on AyT T F T  F    F    T    F    Y     Y Ax=By; Bx msng; transient on AyT T F T  F    F    F    T            Dual non-identical failure on AxByT T F T  F    F    F    F            Nothing matches - triple__________________________________________________________________________                                failure                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T T T F  T    T    T    F    Y Y Y   All match but By missingT T T F  T    T    T    F    Y*                          Y*    Checker failure; distrust BxT T T F  T    T    F    T    Y*                          Y Y   Checker failure; data is fineT T T F  T    T    F    F    Y Y     Ax=Ay; By msng; transient on BxT T T F  T    F    T    T    Y Y Y*  Checker failure; data is fineT T T F  T    F    T    F    Y Y     Bx bad &amp; By missingT T T F  T    F    F    T    Y Y Y   By bad (normal syndrome for By                                msng)T T T F  T    F    F    F    Y Y     Ax=Ay; By msng; transient on BxT T T F  F    T    T    T      Y*                            Y*  Checker failure; distrust AxT T T F  F    T    T    F            By msng &amp; Ay bad =&gt; UncorrectableT T T F  F    T    F    T      Y Y   Ax bad &amp; By missingT T T F  F    T    F    F            Dual non-identical failure on AxAyT T T F  F    F    T    T      Y Y   Bx=Ay; By msng; transient on AxT T T F  F    F    T    F            Dual non-identical failure on BxAyT T T F  F    F    F    T      Y Y   Bx=Ay; By msng; transient on AxT T T F  F    F    F    F            Nothing matches - triple__________________________________________________________________________                                failure                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F F T T  T    T    T    T        Y Y Ax &amp; Ay msng: Bx=ByF F T T  T    T    T    F        Y Y Ax &amp; Ay msng: Bx=ByF F T T  T    T    F    T        Y Y Ax &amp; Ay msng: Bx=ByF F T T  T    T    F    F        Y Y Ax &amp; Ay msng: Bx=ByF F T T  T    F    T    T            Ax &amp; Ay msng: Bx≠ By =&gt;                                UncorrectableF F T T  T    F    T    F            Ax &amp; Ay msng: Bx≠By =&gt;                                UncorrectableF F T T  T    F    F    T            Ax &amp; Ay msng: Bx≠By =&gt;                                UncorrectableF F T T  T    F    F    F            Ax &amp; Ay msng: Bx=By                                =&gt; UncorrectableF F T T  F    T    T    T        Y Y Ax &amp; Ay msng: Bx=ByF F T T  F    T    T    F        Y Y Ax &amp; Ay msng: Bx=ByF F T T  F    T    F    T        Y Y Ax &amp; Ay msng: Bx=ByF F T T  F    T    F    F        Y Y Ax &amp; Ay msng: Bx≠ByF F T T  F    F    T    T            Ax &amp; Ay msng: Bx≠By =&gt;                                UncorrectableF F T T  F    F    T    F            Ax &amp; Ay msng: Bx≠By =&gt;                                UncorrectableF F T T  F    F    F    T            Ax &amp; Ay msng: Bx≠By =&gt;                                UncorrectableF F T T  F    F    F    F            Ax &amp; Ay msng: Bx≠By =&gt;                                Uncorrectable__________________________________________________________________________ *Entry which is different between Integrity and Availability 
    
     
                                           TABLE 3.3__________________________________________________________________________                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T T F F  T    T    T    T    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    T    T    F    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    T    F    T    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    T    F    F    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    F    T    T    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    F    T    F    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    F    F    T    Y Y     Bx &amp; By msng; Ax=AyT T F F  T    F    F    F    Y Y     Bx &amp; By msng; Ax=AyT T F F  F    T    T    T            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    T    T    F            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    T    F    T            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    T    F    F            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    F    T    T            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    F    T    F            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    F    F    T            Bx &amp; By msng; Ax≠Ay =&gt;                                UncorrectableT T F F  F    F    F    F            Bx &amp; By msng; Ax≠Ay =&gt;                                Uncorrectable__________________________________________________________________________                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                    Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F T T F  T    T    T    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  T    T    T    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  T    T    F    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  T    T    F    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  T    F    T    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  T    F    T    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  T    F    F    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  T    F    F    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  F    T    T    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  F    T    T    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  F    T    F    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  F    T    F    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  F    F    T    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  F    F    T    F            Ax &amp; By msng; Bx≠Ay =&gt;                                UncorrectableF T T F  F    F    F    T      Y Y   Ax &amp; By msng; Bx=AyF T T F  F    F    F    F            Ax &amp; By msng; Bx≠Ay =&gt;                                Uncorrectable__________________________________________________________________________                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T F F T  T    T    T    T    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  T    T    T    F    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  T    T    F    T            Bx &amp; Ay msng: Ax≠By =&gt;                                UncorrectableT F F T  T    T    F    F            Bx &amp; Ay msng: Ax≠By ≠&gt;                                UncorrectableT F F T  T    F    T    T    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  T    F    T    F    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  T    F    F    T            Bx &amp; Ay msng: Ax≠By =&gt;                                UncorrectableT F F T  T    F    F    F            Bx &amp; Ay msng: Ax≠By =&gt;                                UncorrectableT F F T  F    T    T    T    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  F    T    T    F    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  F    T    F    T            Bx &amp; Ay msng: Ax≠By =&gt;                                UncorrectableT F F T  F    T    F    F            Bx &amp; Ay msng: Ax≠By =&gt;                                UncorrectableT F F T  F    F    T    T    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  F    F    T    F    Y     Y Bx &amp; Ay msng: Ax=ByT F F T  F    F    F    T            Bx &amp; Ay msng: Ax≠By =&gt;                                UncorrectableT F F T  F    F    F    F            Bx &amp; Ay msng: Ax≠By =&gt;                                Uncorrectable__________________________________________________________________________ *Entry which is different between Integrity and Availability 
    
     
                                           TABLE 3.4__________________________________________________________________________                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F T F T  T    T    T    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    T    T    F    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    T    F    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    T    F    F    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    F    T    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    F    T    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    F    T    F    X X X X Both Ax and Bx msng; No quanta cmprF T F T  T    F    F    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    T    T    T        X X Both Ax and Bx msng; No quanta cmprF T F T  F    T    T    F    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    T    F    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    T    F    F    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    F    T    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    F    T    F    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    F    F    T    X X X X Both Ax and Bx msng; No quanta cmprF T F T  F    F    F    F    X X X X Both Ax and Bx msng; No quanta__________________________________________________________________________                                cmpr                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T F T F  T    T    T    T    X X X X Both Ay and By msng; No quanta cmprT F T F  T    T    T    F    X X X X Both Ay and By msng; No quanta cmprT F T F  T    T    F    T    X X X X Both Ay and By msng; No quanta cmprT F T F  T    T    F    F    X X X X Both Ay and By msng; No quanta cmprT F T F  T    F    T    T    X X X X Both Ay and By msng; No quanta cmprT F T F  T    F    T    F    X X X X Both Ay and By msng; No quanta cmprT F T F  T    F    F    T    X X X X Both Ay and By msng; No quanta cmprT F T F  T    F    F    F    X X X X Both Ay and By msng; No quanta cmprT F T F  F    T    T    T    X X X X Both Ay and By msng; No quanta cmprT F T F  F    T    T    F    X X X X Both Ay and By msng; No quanta cmprT F T F  F    T    F    T    X X X X Both Ay and By msng; No quanta cmprT F T F  F    T    F    F    X X X X Both Ay and By msng; No quanta cmprT F T F  F    F    T    T    X X X X Both Ay and By msng; No quanta cmprT F T F  F    F    T    F    X X X X Both Ay and By msng; No quanta cmprT F T F  F    F    F    T    X X X X Both Ay and By msng; No quanta cmprT F T F  F    F    F    F    X X X X Both Ay and By msng; No quanta__________________________________________________________________________                                cmpr                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________T F F F  T    T    T    T    X X X X Three busses msng; No quanta comprT F F F  T    T    T    F    X X X X Three busses msng; No quanta comprT F F F  T    T    F    T    X X X X Three busses msng; No quanta comprT F F F  T    T    F    F    X X X X Three busses msng; No quanta comprT F F F  T    F    T    T    X X X X Three busses msng; No quanta comprT F F F  T    F    T    F    X X X X Three busses msng; No quanta comprT F F F  T    F    F    T    X X X X Three busses msng; No quanta comprT F F F  T    F    F    F    X X X X Three busses msng; No quanta comprT F F F  F    T    T    T    X X X X Three busses msng; No quanta comprT F F F  F    T    T    F    X X X X Three busses msng; No quanta comprT F F F  F    T    F    T    X X X X Three busses msng; No quanta comprT F F F  F    T    F    F    X X X X Three busses msng; No quanta comprT F F F  F    F    T    T    X X X X Three busses msng; No quanta comprT F F F  F    F    T    F    X X X X Three busses msng; No quanta comprT F F F  F    F    F    T    X X X X Three busses msng; No quanta comprT F F F  F    F    F    F    X X X X Three busses msng; No quanta__________________________________________________________________________                                compr  *Entry which is different between Integrity and Availability 
    
     
                                           TABLE 3.5__________________________________________________________________________                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F T F F  T    T    T    T    X X X X Three busses msng; No quanta comprF T F F  T    T    T    F    X X X X Three busses msng; No quanta comprF T F F  T    T    F    T    X X X X Three busses msng; No quanta comprF T F F  T    T    F    F    X X X X Three busses msng; No quanta comprF T F F  T    F    T    T    X X X X Three busses msng; No quanta comprF T F F  T    F    T    F    X X X X Three busses msng; No quanta comprF T F F  T    F    F    T    X X X X Three busses msng; No quanta comprF T F F  T    F    F    F    X X X X Three busses msng; No quanta comprF T F F  F    T    T    T    X X X X Three busses msng; No quanta comprF T F F  F    T    T    F    X X X X Three busses msng; No quanta comprF T F F  F    T    F    T    X X X X Three busses msng; No quanta comprF T F F  F    T    F    F    X X X X Three busses msng; No quanta comprF T F F  F    F    T    T    X X X X Three busses msng; No quanta comprF T F F  F    F    T    F    X X X X Three busses msng; No quanta comprF T F F  F    F    F    T    X X X X Three busses msng; No quanta comprF T F F  F    F    F    F    X X X X Three busses msng; No quanta__________________________________________________________________________                                compr                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F F T F  T    T    T    F    X X X X Three busses msng; No quanta comprF F T F  T    T    T    F    X X X X Three busses msng; No quanta comprF F T F  T    T    F    T    X X X X Three busses msng; No quanta comprF F T F  T    T    F    F    X X X X Three busses msng; No quanta comprF F T F  T    F    T    T    X X X X Three busses msng; No quanta comprF F T F  T    F    T    F    X X X X Three busses msng; No quanta comprF F T F  T    F    F    T    X X X X Three busses msng; No quanta comprF F T F  T    F    F    F    X X X X Three busses msng; No quanta comprF F T F  F    T    T    T    X X X X Three busses msng; No quanta comprF F T F  F    T    T    F    X X X X Three busses msng; No quanta comprF F T F  F    T    F    T    X X X X Three busses msng; No quanta comprF F T F  F    T    F    F    X X X X Three busses msng; No quanta comprF F T F  F    F    T    T    X X X X Three busses msng; No quanta comprF F T F  F    F    T    F    X X X X Three busses msng; No quanta comprF F T F  F    F    F    T    X X X X Three busses msng; No quanta comprF F T F  F    F    F    F    X X X X Three busses msng; No quanta__________________________________________________________________________                                compr                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F F F T  T    T    T    F    X X X X Three busses msng; No quanta comprF F F T  T    T    T    F    X X X X Three busses msng; No quanta comprF F F T  T    T    F    T    X X X X Three busses msng; No quanta comprF F F T  T    T    F    F    X X X X Three busses msng; No quanta comprF F F T  T    F    T    T    X X X X Three busses msng; No quanta comprF F F T  T    F    T    F    X X X X Three busses msng; No quanta comprF F F T  T    F    F    T    X X X X Three busses msng; No quanta comprF F F T  T    F    F    F    X X X X Three busses msng; No quanta comprF F F T  F    T    T    T    X X X X Three busses msng; No quanta comprF F F T  F    T    T    F    X X X X Three busses msng; No quanta comprF F F T  F    T    F    T    X X X X Three busses msng; No quanta comprF F F T  F    T    F    F    X X X X Three busses msng; No quanta comprF F F T  F    F    T    T    X X X X Three busses msng; No quanta comprF F F T  F    F    T    F    X X X X Three busses msng; No quanta comprF F F T  F    F    F    T    X X X X Three busses msng; No quanta comprF F F T  F    F    F    F    X X X X Three busses msng; No quanta__________________________________________________________________________                                compr 
    
     
                                           TABLE 3.6__________________________________________________________________________                        AvailabilityQuanta Received    Syndrome            Quanta ValidAx  Ay    Bx By Ax=Ay         Bx=By              Ax=By                   Bx=Ay                        Ax                          Ay                            Bx                              By                                Reason__________________________________________________________________________F F F F  T    T    T    T    X X X X All busses msng; No quanta comprF F F F  T    T    T    F    X X X X All busses msng; No quanta comprF F F F  T    T    F    T    X X X X All busses msng; No quanta comprF F F F  T    T    F    F    X X X X All busses msng; No quanta comprF F F F  T    F    T    T    X X X X All busses msng; No quanta comprF F F F  T    F    T    F    X X X X All busses msng; No quanta comprF F F F  T    F    F    T    X X X X All busses msng; No quanta comprF F F F  T    F    F    F    X X X X All busses msng; No quanta comprF F F F  F    T    T    T    X X X X All busses msng; No quanta comprF F F F  F    T    T    F    X X X X All busses msng; No quanta comprF F F F  F    T    F    T    X X X X All busses msng; No quanta comprF F F F  F    T    F    F    X X X X All busses msng; No quanta comprF F F F  F    F    T    T    X X X X All busses msng; No quanta comprF F F F  F    F    T    F    X X X X All busses msng; No quanta comprF F F F  F    F    F    T    X X X X All busses msng; No quanta comprF F F F  F    F    F    F    X X X X All busses msng; No quanta__________________________________________________________________________                                compr