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.>

We explore the nature of incomplete specification in sequential circuits. We compare it to the case of combinational circuits and propose new definitions and algorithms. We extend the existing algorithms for input don't care sequences and provide a new theory for output don't care sequences, based on the concept of information lossyness. The implementation of the proposed techniques in a program called SEQUOIA (sequential optimization of interacting automata) shows that our approach is viable and effective.>

computing synchronizing sequences is an important step in experimental results that show the viability of the proposed method for much larger circuits than were tractable by previous exact methods.

A. Grasselli and F. Luccio (1965) proved that a minimum state cover of an incompletely specified finite-state machine could be found by only considering prime compatibles. It was conjectured that in practice one could restrict even further the set of compatibles being considered to the set of maximal compatibles. The conditions under which a solution formed of maximal compatibles was guaranteed to be exact were determined, but the question of the practical relevance of prime compatibles remained open. It is shown here that state minimization problems which require the full generality afforded by prime compatibles for the solution to be optimal are actually found in practice. The proof relies on the concept of analogous machines-essentially machines that pose the same minimization problem. The main result is that for any incompletely specified machine there is an analogous machine that has to be minimized in the optimization of two interacting, completely specified machines. >

The authors consider the nature of incomplete specifications for a finite state machine embedded in a network of sequential machines. They show how limited controllability and observability of component machines are expressed in quite different ways. For the input don't care sequences, a general solution was known. The authors present extensions to it, both in terms of topologies contemplated and in terms of applicability to larger designs. For the output don't care sequences, they provide a general theory based on the concept of information lossyness and present algorithms to address the related optimization problem in practical cases. The implementation of the proposed techniques in a program called SEQUOIA (sequential optimization of interacting automata) shows that the proposed approach is viable and effective.>