关于部分多值逻辑函数集中准完备集的若干性质

摘要

The simplest decision on Sheffer function is an important theoretical and practical problem in structure theory of multiple-valued logic functions. According to the system perspecc-tive of "preserving relationship", this paper discussed some properties of pre-complete classes of some multiple-valued logic function sets by means of group theory and combinatorial mathemat-ics. The necessary and sufficient conditions satisfying that the non-empty relationship is a totally relationship and the subgroup H is the symmetric group of Gm are found and proofed. In addition, the number of the complete symmetric function sets in Fs.m is presented. The obtained results provide some basis for judging Sheffer functions in partial multiple-valued logic.%Sheffer函数的最简判定是多值逻辑函数集完备性判定问题中的一个重要的理论和实际问题.文中根据多值逻辑函数理论中“保关系”的系统思想,使用群论和组合数学的工具,研究了部分多值逻辑函数集中准完备类相应关系的若干性质.给出并证明了非空关系Gm是完全关系以及子群H是Gm的对称群的充要条件,定出了部分k值逻辑中完满对称函数类Fs,m中函数集的个数.以上工作为解决部分多值逻辑中Sheffer函数的判定提供了研究基础.