A new algorithm for exact reduction of incompletely specified finite state machines

We propose a new algorithm for the problem of state reduction in incompletely specified finite state machines. Unlike the most commonly used algorithms for this problem, our approach is not based on the enumeration of compatible sets, and, therefore, its performance is not dependent on its number. Instead, the algorithm uses techniques for finite state machine identification that are well known in the computer science literature, but have never been applied to this problem. We prove that the algorithm is exact and present results that show that, in a set of hard problems, it is much more efficient than both the explicit and implicit approaches based on the enumeration of compatible sets. We also present a complexity analysis for the special cases where worst case polynomial time bounds can be obtained and present experiments that validate empirically the bounds obtained.