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Simplification of Incompletely Specified Flow Tables with the Help of Prime Closed Sets
October 1969 (vol. 18 no. 10)
pp. 953-956
In this short note, an attempt has been made to arrive at a general algorithm for minimizing the number of internal states in an incompletely specified flow table. The closure property of the compatibility classes which cover a given flow table leads us to the derivation of a particular class of closed sets defined as irredundant prime closed sets. It has been shown that these prime closed sets in sequential circuit synthesis play an analogous role to that of the prime implicants in combinational circuit synthesis. A method has been described for determining all the irredundant prime closed sets and finding the minimal row flow table by suitably choosing one or a collection of those sets.
Index Terms:
Class set, closed set, closure condition table, compatibility class, cover chart, flow table, implication table, maximum compatibility class, minimal cover, prime closed set, prime compatibility class, redundant and irredundant prime closed sets, states of a flow table.
Citation:
S.C. De Sarkar, A.K. Basu, A.K. Choudhury, "Simplification of Incompletely Specified Flow Tables with the Help of Prime Closed Sets," IEEE Transactions on Computers, vol. 18, no. 10, pp. 953-956, Oct. 1969, doi:10.1109/T-C.1969.222552
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