Research On The Some Properties Of Precomplete Classes In Partial Multiple-Valued Lgic Function Sets

Multiple-valued logic is the logic that has more than two values. It includes three research parts, which is the theory, circuit & system, and its applications.The structure theory of multiple-valued logic functions includes completeness theory, function denotation theory, and unidirectional trapdoor function. One of the most important and fundamental problems is the completeness decision on function sets, it is also the problem which must be solved in automata theory and multiple-valued logic net work. The solution of this problem depends on determining all the precomplete classes in multiple-valued logic function sets. Another important problem in multiple-valued logic completeness theory is the decision on Sheffer function, which depends on deciding the minimal covering of the precomplete classes. For the complete multiple-valued logic functions, it was solved. However, for the partial multiple-valued logic functions, it has not been solved thoroughly.In this thesis, some properties of precomplete classes and regular relation in partial multiple-valued logic are researched. It laid the foundation for the decision on minimal covering of precomplete sets in partial multiple-valued logic.In this thesis, we first introduce the basic concept and important achievement, then, we present some results on classification and minimal covering of precomplete classes, concept of similariy relation and property among precomplete sets preserving similariy relation, at last, we give some properties of some precomplete classes and regular relation in partial multiple-valued logic and their proof.