A fully implicit algorithm for exact state minimization

Abstract

State minimization of incompletely specified machines is an important step of FSM synthesis. An exact algorithm consists of generation of prime compatibles and solution of a binate covering problem. This paper presents an implicit algorithm for exact state minimization of FSM's. We describe how to do implicit prime computation and implicit binate covering. We show that we can handle sets of compatibles and prime compatibles of cardinality up to 2 1500 . We present the first published algorithm for fully implicit exact binate covering. We show that we can reduce and solve binate tables with up to 10 6 rows and columns. The entire branch-and-bound procedure is carried on implicitly. We indicate also where such examples arise in practice.

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“…Recent research in the field of logic synthesis (Coudert, Berthet & Madre, 1989) and discrete optimization (Kam et al, 1994) has shown that implicit enumeration algorithms can be very effective in dealing with search problems with extremely large search spaces. Implicit enumeration algorithms are based on the idea of replacing the explicit search for a solution by a description, in implicit form, of a function describing all the possible solutions.…”

Optimal state reductions of automata with partially specified behaviors

“…The first algorithm for the exact solution was described by Paull and Unger [11], and Pfleeger [13] proved that the minimization of incomplete deterministic Moore machines is a NP-complete problem. Since then many other exact and heuristic algorithms have been proposed, some considering that the initial machine is nondeterministic [14,8,12,9,3]. The standard Paull and Unger approach is based on the identification of sets of compatible states and the obtention of a minimal closed cover.…”

Sequential synthesis using S1S

“…This general framework also strictly subsumes the problem considered in [35]. Compared to supervisory control of DES [25], our approach offers the advantage of being compatible with FSM techniques that have seen continuous developments in the past three decades (e.g., [16] and [35]), provides more natural model of reactive system, and allows significantly simpler development of results.…”