Fault detection in sequential machines

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1972

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Abstract

Sequences and techniques useful in the design of checking experiments are examined. Necessary and sufficient conditions are formulated for a machine to possess distinguishing and synchronizing sequences. Least upper bounds are placed upon the length of repeated symbol distinguishing and repeated symbol synchronizing sequences. An improperly designed test sequence for the state identification phase of a checking experiment is given to illustrate a faulty machine which is not detected. The restrictions necessary to impose upon machines to make the testing problem tractable are discussed. It is shown these restrictions are not overly burdensome. Some useful properties of compound distinguishing sequences are proved. Characterizing sequences are examined in detail and a previous bound is reduced by 50 percent to obtain the least upper bound on their total length. The reduced bounds on characterizing sequences are used in the construction of locating sequences. A series of theorems puts the locating sequence concept on a firm theoretical foundation. The precise conditions needed to insure locating sequences always transfer a machine to the same state are delineated and proved. Better use is made of the strong connectedness of tested machines to achieve a 50 percent reduction over previous bounds on the length of transfer sequences. Both the reduced bounds on characterizing and on transfer sequences are used to derive a bound smaller than those published on the length of checking experiments for a machine possessing a simple I/O sequence and a valid homing sequence. A resettable machine with and without a unique output terminal to identify the reset state is examined to determine the effect of the reset feature upon the length of checking experiments for machines possessing valid homing, distinguishing, and locating sequences. It is shown that resettable machines possessing valid homing sequences achieve about a 20 percent reduction over bounds derived for non-resettable machines. Resettable machines possessing distinguishing sequences achieve about a 50 percent reduction over non-resettable machines, and resettable machines possessing only locating sequences achieve about a 95 percent reduction over the non-resettable machine. In each of the above classes of machines, no assumptions are made on the correct operation of the reset feature. Instead the machine's reset is thoroughly tested as an integral part of the checking experiment. The experiment design procedures and the upper bound derivations are clearly given to illustrate the testing advantages inherent in each of the classes of resettable machines examined.

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