A method for general simultaneous full decomposition of sequential machines : algorithms and implementation

TLDR: The preliminary results are promising, because in all the checked cases the method was able to discover the natural decompositional structure of the sequential machine by a very limited search; however, checking the method on larger samples of machines is still necessary in order to obtain more complete and more reliable information on the performance of the method.

Abstract: Sequential machines that specify the control units and serial processing units of today's digital systems are quite complex and therefore designing, optimising, implementing and testing them is a complicated matter. This is the reason for the great interest in methods and CAD-tools for decomposing the complex machines into smaller and less complex ones. One of the decomposition sorts feasible for sequential machines is a general simultaneous full decomposition. In this decomposition the sequential machine is decomposed into a number of simultaneously worldng partial machines which are able to interact, each with the other ones, and to realise together the behaviour of the original machine. There are no constraints on the direction of the interconnections between the partial machines and the total machine's behaviour is decomposed, i.e. not only the state set, but the input and output sets as well. The aim of the reported research was to develop, implement and test an efficient heuristic method for the general simultaneous full decomposition of Moore machines with encoded inputs and outputs and symbolic states. It is required that the method will be able to discover the natural decompositionaI structure of the sequential machine. As a result a method has been developed, implemented and tested which constructs the limited set of near-optimal decompositions using a beam search bottom-up hierarchical clustering algorithm, with decision making based on correlations between the information flows in the sequential machine. In order to get an impression about the performance of the method, a number of experiments has been performed. In these experiments some machines have been used with a known optimal decompositionai structure and other machines have been taken from the international benchmark set [18]. The preliminary results are promising, because in all the checked cases, the method was able to discover the natural decompositional structure by a very limited search; however, checking the method on larger samples of machines is still necessary in order to obtain more complete and more reliable information on the performance of the method.