Stochastic testing of finite state machines

This paper discusses an approach that uses statistical observations about the steady-state behavior of a finite state machine (FSM) in order to detect and identify permanent failures in its state transition mechanism. The intended application domain is in testing/monitoring digital dynamic systems against permanent failures, such as manufacturing defects or stuck-at faults. In order to test for the correctness of the state transition function of a given FSM, we apply inputs that are chosen according to some fixed probability distribution. We show that by analyzing perturbations in the steady-state probabilities of different states, one can detect and identify permanent changes in the state transition function. The proposed technique only requires knowledge of the input probability distribution and the steady-state reached by the FSM, and can potentially be used in testing/monitoring of distributed systems (where the exact order of inputs, states and outputs may not be known) or in systems with observability constraints in their inputs, states and/or outputs