State Minimization of PNDFSMs in Networks of FSMs

Abstract

A behavior is permissible at a node of an interconnection, say at M ₁, if the system obtained by placing at that node a DFSM that represents the behavior works according to the original specification. Such a replacement is allowed if the composition is well-defined and the global behavior is the one expected. Unfortunately not any behavior contained in a PNDFSMs is permissible, i.e., it is valid candidate for implementation. The reason is that it may not yield a well-defined feedback composition. Watanabe proposed in [119] a sufficient condition in the form of acyclicity, for a behavior to be permissible. In the previous chapter, we have presented a comprehensive analysis of the conditions for the existence of a correct feedback composition, and described how to find all valid candidate behaviors. Since a valid candidate is preferred if it minimizes the number of states of the related FSM, here we will discuss the problem of the combined objective of finding a state-minimum and well-defined behavior.