A Method for Minimizing Incompletely Specified Sequential Machines

After Paull and Unger introduced the problem of state minimization in incompletely specified sequential machines (ISSM's), its increasing importance and complexity induced many people to continue research related to this field. Here we shall present a method for obtaining a minimum form of a given ISSM by application of a directed tree graph. In order to save counting effort for a minimum form, we extend the concept of erasure from a relation between compatibles to one between subsets of compatibles. The use of the extended erasure rules can prune the directed tree graph effectively to find a minimum form of a given ISSM. Furthermore, by utilizing the concept of maximal incompatible (MI) we can determine a lower bound for the state number of the minimum form of a given ISSM, and also effectively control the initial steps in generating the directed tree graph.