LOGIC FUNCTIONS AND SEQUENTIAL MACHINES.
POLYTECHNIC INST OF BROOKLYN N Y MICROWAVE RESEARCH INST
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The paper presents the application of an algebra of logic functions for the finding of the homomorphic images of sequential machines and leads to some of their decompositions and assignments. The main idea is the formation of groups of internal states from the machine flow-table by application of the concentration, which is the main tool of a new algebra of logic functions generalizing the concensus theory. A variable, called the grouping variable, has been defined and studied. It is more general than the well-known partition which is only one of its homomorphisms. To each machine we can associate a merging function which stresses the correspondence between each possible grouping of the internal states and a sufficient partition allowing this grouping. Each implicant of this function is similar to a partition pair in the sense of Hartmanis and Karp. The principal implicants which are the prime implicants of the merging function, related to binary partitions, can be easily computed. These partitions give the principal groups of states for the machine which play an essential role in finding the simplest homomorphisms, assignments, and machine decompositions.
- Theoretical Mathematics
- Computer Hardware