Abstract
A mathematical framework for the testing and diagnosis of sequential machines is developed. A very general fault model is used in which a faulty machine is represented as a sequential machine, possibly with state and output sets different from those of the good machine. A deterministic finite automaton, called observer, describes the process by which one gains information from the observation of the responses to test sequences. It generalizes the work of Hennie on distinguishing and homing sequences, by modelling all the possible conclusions that could be drawn from observing the circuit under test. A nondeterministic acceptor is derived from the observer; it accepts diagnosing sequences and can also be used to generate test sequences. We then associate probabilities with this nondeterministic acceptor which, together with a stochastic source of input symbols, provides a probabilistic diagnoser. As a particular application we consider the testing and diagnosis of random-access memories by random test sequences. Our model generalizes the work by David et al. on the calculation of the length of a random test sequence required to guarantee that the probability of detection of a fault exceeds a prescribed threshold.
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J.A. Brzozowski, H. Jürgensen, “Deterministic Diagnosis of Sequential Machines.” Proc. 2nd Conf. on Automata, Languages, and programming Systems, Salgótarján, Hungary, F. Gécseg and I. Peák, eds. Department of Mathematics, Karl Marx University of Economics, Budapest, 1988–4, 1988, 35–49.
J.A. Brzozowski, H. Jürgensen, “Probabilistic Diagnosis of Sequential Machines.” Proc. 2nd Conf. on Automata, Languages, and Programming Systems, Salgótarján, Hungary, F. Gécseg and I. Peák, eds. Department of Mathematics, Karl Marx University of Economics, Budapest, 1988–4, 1988, 51–66.
J.A. Abraham, V.K. Agarwal, “Test Generation for Digital Systems,” in (D.K. Pradhan, eds.) Fault-Tolerant Computing, Prentice-Hall, Englewood Cliffs, NJ, 1986, pp. 1–90.
H. Fujiwara, Logic Testing and Design for Testability, MIT Press, Cambridge, 1985.
R. David, A. Fuentes, B. Courtois, “Random pattern testing versus deterministic testing of RAMS,” IEEE Trans. on Comp. vol. C-38, pp. 637–650, May 1989.
R. David, A. Fuentes, “Fault diagnosis of RAM's from random testing experiments,” IEEE Trans. on Comp, vol. C-39, pp. 220–229, February 1990.
A. Fuentes, R. David, B. Courtois, “Random testing versus deterministic testing of RAMS,” Proc. of the 16th Int. Symp. on Fault Tolerant Comp. Systems, IEEE, pp. 266–271, 1986.
A. Fuentes, Contribution à l'étude du test aléatoire de memoires RAM. Thèse, Institut National Polytechnique de Grenoble, 1986.
A.A. Ismaeel, M.A. Breuer, “The probability of error detection in sequential circuits using random test vectors,” J. Electronic Testing: Theory and Applications vol. 1 pp. 245–256, 1991.
P.H. Starke, Abstract Automata, North-HollandAmsterdam, 1972.
D. Wood, Theory of Computation, Harper & Row, New York, 1987.
J.F. Poage, E.J. McCluskey, “Derivation of optimum test sequences for sequential machines,” Proc. of the 5th Annual Symp. on Switching Theory and Logical Design, IEEE, pp. 121–132, November 1964.
F.C. Hennie, “Fault-detecting experiments for sequential circuits,” Proc. of the 5th Annual Symp. on Switching Theory and Logical Design, IEEE, pp. 95–110, November 1964.
S. Graf, M. Gössel, Fehlererkennungsschaltungern. Akademie-Verlag, Berlin, 1987.
R. David, J.A. Brzozowski, H. Jürgensen, “Testing for bounded faults in RAMs,” Research Report CS-92-30, Department of Computer Science, University of Waterloo, 1992.
F.C. Hennie, Finite-State Models for Logical Machines, John Wiley & Sons, New York, 1968.
M. Yannakakis, D. Lee, “Testing finite state machines,” Proc. 23rd Annual ACM Symp. on Theory of Computing, ACM, New York, pp. 476–485, 1991.
W. Feller, An Introduction to Probability Theory and Its Applications, John Wiley & Sons, New York, 1968 (3rd edition).
J.L. Doob, Stochastic Process, John Wiley & Sons, New York, 1953.
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This work was supported by the Natural Sciences and Engineering Research Council of Canada, Grants OGP0000871 and OGP0000243, and a grant from the Information Technology Research Centre of Ontario. Preliminary papers leading to this work have appeared earlier [1] [2].
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Brzozowski, J.A., Jürgensen, H. A model for sequential machine testing and diagnosis. J Electron Test 3, 219–234 (1992). https://doi.org/10.1007/BF00134732
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DOI: https://doi.org/10.1007/BF00134732