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Minimization of Incompletely Specified Sequential Machines
November 1975 (vol. 24 no. 11)
pp. 1089-1100
C.V.S. Rao, School of Automation, Indian Institute of Science
A simple yet efficient method for the minimization of incompletely specified sequential machines (ISSM's) is proposed. Precise theorems are developed, as a consequence of which several compatibles can be deleted from consideration at the very first stage in the search for a minimal closed cover. Thus, the computational work is significantly reduced. Initial cardinality of the minimal closed cover is further reduced by a consideration of the maximal compatibles (MC's) only; as a result the method converges to the solution faster than the existing procedures. "Rank" of a compatible is defined. It is shown that ordering the compatibles, in accordance with their rank, reduces the number of comparisons to be made in the search for exclusion of compatibles. The new method is simple, systematic, and programmable. It does not involve any heuristics or intuitive procedures. For small- and medium-sized machines, it can be used for hand computation as well. For one of the illustrative examples used in this paper, 30 out of 40 compatibles can be ignored in accordance with the proposed rules and the remaining 10 compatibles only need be considered for obtaining a minimal solution.
Index Terms:
Basic compatible, deletion of compatibles, exclusion of compatibles, incompletely specified sequential machine, minimal closed cover, min-max cover, primary compatible, prime closed sets of compatibles, rank of a compatible, symbolic compatible.
Citation:
C.V.S. Rao, N.N. Biswas, "Minimization of Incompletely Specified Sequential Machines," IEEE Transactions on Computers, vol. 24, no. 11, pp. 1089-1100, Nov. 1975, doi:10.1109/T-C.1975.224137
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