Decomposition of synchronous sequential machines into synchronous and asynchronous submachines

Abstract

The problem of the decomposition of a sequential machine into smaller submachines has been treated by Hartmanis (1961, 1962) through the algebra of partitions. Using partitions, we have faced the problem of the decomposition of a synchronous sequential machine into a state synchronous machine, a state asynchronous machine, and a combinational output circuit. Two types of decomposition are studied: (1) the serial decomposition in which the synchronous submachine drives the asynchronous one, and (2) the parallel decomposition. The problem of the physical realization of a synchronous machine having a nontrivial serial or parallel decomposition is examined, and it is shown that these decompositions are useful for economical realizations since they reduce the number of delay elements necessary for storing the internal state of the machines. Synchronous machines considered in this paper are chiefly of the Mealy and Moore type. However, another type of synchronous machine is defined which is found to be of particular interest for the decompositions studied.