The Decision On The Minimal Covering Of Function Sets Preserving Ternary And Quaternary 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. The solution of this problem depends on determining all the precomplete classes (i.g. maximal closed sets) in multiple-valued logic function sets.The decision on Sheffer function is an important problem in multiple-valued logic completeness theory, which depends on deciding the minimal covering of the precomplete classes. For the complete multiple-valued logic functions, it was solved by Schofield and Kudrjavcev etc. For the partial multiple-valued logic functions, it has not been solved thoroughly.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 ternary and quaternary regularly separable relations.The thesis is divided into five chapters. In chapter one, it mainly introduces the background and source of the subject, and summarizes the main work of my task.In the second chapter, it summarizes the structure theory of multiple-valued logic functions. First, it introduces the basic concept and important research results of the structure theory of the complete multiple-valued logic functions, and then it introduces the precomplete class in the partial k-valued logic functions and the decision on Sheffer function. Finally, concludes the results in the decision on the minimal covering of the partial multiple-valued logic function sets.In the third chapter, according to the property of similar relationship,it proves 10 classes of function sets which sum to 84 preserving ternary regularly separable relations are not belong to the minimal covering of precomplete function sets in P4 *, and proves the another 8 classes of function sets which sum to 36 must be the minimal covering of precomplete function sets in P4 *.In the fourth chapter, it proves 29 classes of function sets which sum to 67 preserving quaternary regularly separable relations are not belong to the minimal covering of precomplete function sets in P4 *, and proves the another 22 classes of function sets which sum to 42 must be the minimal covering of precomplete function sets in P4 *.And find out the minimal covering of function sets preserving regularly separable relations in partial four-valued logic.In the fifth chapter, it educes some Sheffer functions in P4 *.