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Abstractions of Finite-State Machines Optimal with Respect to Single Undetectable Output Faults
February 1987 (vol. 36 no. 2)
pp. 185-200
K.N. Oikonomou, AT&T Information Systems
An observer, whose task is to monitor a large and complex system M^ subject to malfunctions, may be interested in dealing with a simplified, abstracted model (M^A of it, at the expense of some loss in fault-detection ability. Let M^ be a finite- state machine whose inputs are modeled by stationary random variables. The abstraction A is effected by lumping M^'s states, inputs, and outputs into classes, to obtain a smaller probabilistic machine M^A. These ideas have been introduced in a previous paper, and the question of finding an optimal abstraction A* which minimizes the number of faults undetectable by the observer was posed. An algorithm for constructing the output component of the optimal abstraction A* is given in this paper. If there are no faults in the next-state map of M^, this construction is sufficient to minimize the number of single faults in the output map that are undetectable by the observer because of the abstraction. Some experiments carried out using the algorithm provide general insight into the tradeoff between simplifying M^ and making some faults in it undetectable. As a specific example, optimal output abstractions are found for a finite-state machine specification of the link level of the X.25 communication protocol.
Index Terms:
undetectable output faults, Abstraction, branch-and-bound algorithm, finite-state machine, observer, optimal abstraction
Citation:
K.N. Oikonomou, "Abstractions of Finite-State Machines Optimal with Respect to Single Undetectable Output Faults," IEEE Transactions on Computers, vol. 36, no. 2, pp. 185-200, Feb. 1987, doi:10.1109/TC.1987.1676881
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