Exact and heuristic algorithms for the minimization of incompletely specified state machines

In this paper we present two exact algorithms for state minimization of FSM's. Our results prove that exact state minimization is feasible for a large class of practical examples, certainly including most hand-designed FSM's. We also present heuristic algorithms, that can handle large, machine-generated, FSM's. The possibly many different reduced machines with the same number of states have different implementation costs. We discuss two steps of the minimization procedure, called state mapping and solution shrinking, that have received little prior attention to the literature, though they play a significant role in delivering an optimally implemented reduced machine. We also introduce an algorithm whose main virtue is the ability to cope with very general cost functions, while providing high performance. >