The Decision On The Minimal Covering Of Function Sets Preserving Fully Symmetric Relation In Partial 4-Valued Logic

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 of function sets. 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 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 decision on minimal covering of precomplete classes in partial multiple-valued logic. We focus on function sets preserving full symmetric relation and prove that 46 function sets preserving full symmetric relation must be the component part of the minimal covering of precomplete classes in P4 * by means of the concept of similar relationship among precomplete sets.The thesis is divided into four chapters. The first chapter is a foreword. It introduces the history and aspect of researching multiple-valued logic. And then, it summarizes the new effort of researching multiple-valued logic.In the second chapter, it summarizes the structure theory of multiple-valued logic functions. First, it introduces the basic concept 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.In the third chapter, it introduces the minimal covering of precomplete class in partial k-valued logic. First, it introduces the concept of minimal covering and the relation between the concept and decision problem of Sheffer function. Then, it introduces the concept of similar relation among the precomplete sets, summarizes the research status and main production of minimal covering of precomplete classes in P_k~*.In the fourth chapter, it studies the function set preserving full symmetric relation in partial four-valued logic, 78 precomplete classes are sorted according to similar relationship, 32 precomplete classes are weeded out, 10 functions are constructed,46 precomplete classes are proved the component part of the minimal covering.