Testing Finite State Machines: Fault Detection

Abstract

We present simple randomized algorithms for the fault detection problem: Given a specification in the form of a deterministic finite state machine A and an implementation machine B, determine whether B is equal to A. If A has n states and p inputs, then in randomized polynomial time we can construct with high probability a checking sequence of length O(pn4 log n), i.e., a sequence that detects all faulty machines with at most n states. Better bounds can be obtained in certain cases. The techniques generalize to partially specified finite state machines.