State minimization of pseudo non-deterministic FSMs

This paper is concerned with the problem of optimizing a system of interacting finite state machines (FSMs). It has been shown previously by the authors that the complete set of sequential behaviors that can be implemented at a particular component of the system can be computed and represented by a single non-deterministic FSM, called the E-machine. In this paper, we consider the problem of finding an optimum behavior for the component, which is given by minimizing the E-machine, where the cost function is the number of states required for representing a behavior. We first present a theoretical analysis, in which we show the E-machine has a special property called pseudo nondeterminism, and this property can be effectively used for solving the problem. We then propose a heuristic method. The algorithm has been implemented, and initial experiments are given