Closure Partition Method for Minimizing Incomplete Sequential Machines

A new method based on a closure partition over a set of some compatibles is proposed for selecting a minimal machine from mutualy independent closure aggregates by simply checking only the trivial covering condition. The closure aggregates are derived from some closure related classes. The latter classes are derived from the closure classes by replacing aU superseded elements with their greatest superseding ones. The compatibles to be considered are some subsets of maximum compatibles related under the state transition or the set inclusion. Closure dependent classes may contain superseded and redundant compatibles but their corresponding closure aggregates have only unsuperseded and irredundant elements. Both of them are closed. However, some closure related class may not be closed and may contain some redundant elements. The remaining unrelated subsets of maximum compatibles are ignored. Superseded or redundant compatibles when they are so determined are also ignored. Thus possible candidates for irredundant closed covers can be yielded and then partitioned under the closure dependence relation.