| 关于部分多值逻辑函数集中准完备集的若干性质 |
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| 引用本文： | 刘任任,王婷,谭昊勋.关于部分多值逻辑函数集中准完备集的若干性质[J].计算机学报,2012,35(4):754-760. |
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| 作者姓名： | 刘任任 王婷 谭昊勋 |
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| 作者单位： | 1. 湘潭大学信息工程学院 湖南湘潭411105;智能计算与信息处理教育部重点实验室(湘潭大学) 湖南湘潭411105
2. 湘潭大学能源工程学院 湖南湘潭411100 |
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| 基金项目： | 国家自然科学基金，湖南省重点学科建设项目，湖南省科技厅计划，湖南省教育厅科学基金，湘潭大学自然科学基金 |
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| 摘 要： | 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.
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| 关 键 词： | 多值逻辑 完备性 保关系 准完备集 Sheffer函数 |
Some Properties on Precomplete Classes in Partial Multiple-Valued Logic Function Sets |
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| Liu Ren-Ren
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WANG Ting
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Tan Hao-Xun.Some Properties on Precomplete Classes in Partial Multiple-Valued Logic Function Sets[J].Chinese Journal of Computers,2012,35(4):754-760. |
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| Authors: | Liu Ren-Ren WANG Ting Tan Hao-Xun |
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| Affiliation: | 1)(School of Information Engineering,Xiangtan University,Xiangtan,Hunan 411105) 2)(Key Laboratory of Intelligent Computing & Information Processing(Xiangtan University), Ministry of Education,Xiangtan,Hunan 411105) 3)(School of Energy Engineering of Xiangtan University,Xiangtan,Hunan 411100) |
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| Abstract: | 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 perspective 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 mathematics.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. |
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| Keywords: | multiple-valued logic completeness preserving relation pre-complete classes Sheffer functions |
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