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Polylinear Decomposition of Synchronous Sequential Machines
December 1978 (vol. 27 no. 12)
pp. 1144-1152
C. Halatsis, Digital Systems Laboratory, Computer Center, Nuclear Research Center
The paper presents systematic procedures for decomposing a sequential machine into submachines some or all of which are realized by polylinear sequential circuits. This polylinear decomposition is based upon classes of subsets of the set of states which possess the substitution property rather than upon partitions with substitution property. These classes are easily found using the backward state transition function of the machine and enables one to treat uniformly and simultaneously the problems of state minimization, machine decomposition in the classical or the polylinear way, finding the lattice of the partitions with substitution property, and periodic decomposition based upon classes that correspond to cyclic partitions. Procedures are developed for deriving optimal all polylinear decompositions and "good" partial polylinear decompositions of a machine.
Index Terms:
synchronous sequential machines, Backward state transition function, connected class, lattice of partitions with substitution property, periodic decomposition, polylinear decomposition, state minimization, strongly connected class
C. Halatsis, M. Sigala, G. Philokyprou, "Polylinear Decomposition of Synchronous Sequential Machines," IEEE Transactions on Computers, vol. 27, no. 12, pp. 1144-1152, Dec. 1978, doi:10.1109/TC.1978.1675017
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