SECONDARY STATE ASSIGNMENT AND DECOMPOSITION OF SEQUENTIAL MACHINES.
POLYTECHNIC INST OF BROOKLYN NY MICROWAVE RESEARCH INST
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In the first part of the paper a method is developed to obtain for any given machine M which is in reduced form and undecomposable an equivalent machine M which possesses a partition with substitution property or partition pairs. Therefore, a state assignment or assignments with reduced dependency exist for M. The method requires augmentation of the original machine M by a technique of state-splitting. It should be noted that the augmentation does not necessarily increase the complexity of the logic required for the implementation and, in fact, often reduces it. The problem of finding cascade decompositions for two or more reduced machines which have the same input, such that a common submachine may be factored out and serve as a predecessor machine feeding two or more successor machines is examined. Necessary and sufficient conditions under which it is possible to obtain decompositions which contain such a common submachine are developed. If the given machines do not satisfy these conditions, and a common submachine cannot be found, it is shown how one or both machines can be replaced by equivalent machines in such a way that some common submachine can be found. A systematic method has been developed for the determination of the common factor. The basic tool, in this study is the composite machine CM which is derived from the original machines. The properties of the CM are studied and the maximal common factor is obtained with a minimum of computation or manipulation. Author
- Operations Research