Polylinear Decomposition of Synchronous Sequential Machines

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.