The Decision On The Minimal Covering Of Function Sets Preserving Binary Regularly Separable Relations In Partial Four-Valued Logic

Multiple-valued logic is an important branch of computer science. With the progress of computer science and technology multiple-valued logic got unprecedented development. It includes the research of the theory, circuit & system, and its applications. The completeness of multiple-valued logic function is an important subject of multiple-valued logic theory.In the theory of partial multiple-valued logic, a primary and important problem is the completeness of function sets, which can be solved depending on the decision for all the precomplete sets of partial K-valued function sets noted by PK *. Another important problem is the decision of Sheffer functions, which can be solved by finding out all of the minimal covering of the precomplete sets.The main work of this thesis is the decision on the minimal covering of precomplete sets in partial four-valued logic. We focus on the decision in the minimal covering of function sets preserving binary regularly separable relations.The thesis is divided into four chapters. In the first chapter, it introduces the basic concepts and important research results of the multiple-valued logic function theory, focuses on the regularly separable functions of the partial multiple-valued logic function theory, and concludes the results in the decision on the minimal covering of the partial multiple-valued logic function sets.In the second chapter, it finds out all precomplete sets of regularly separable relations in partial four-valued logic and classifies them by the resemble relations theory.In the third chapter, it finds out 370 sets which not belong to the minimal covering of function sets in regularly separable relations in partial four-valued logic.In the fourth chapter, it finds out 277 sets which may belong to the minimal covering of partial four-valued logic and proves that 48 regularly separable sets belong to the minimal covering in the partial four-valued logic when m=2.