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| 概率有限自动机积的覆盖性 |
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杨京开1,2,蔡永裕3,程裕强1,黄飞丹41,2,3,4
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1.玉林师范学院 数学与统计学院,广西 玉林 537000;2.玉林师范学院 广西高校复杂系统优化与大数据处理重点实验室,广西 玉林 537000;3.湖南科技大学 数学与计算科学学院,湖南 湘潭 411201;4.贵州工程应用技术学院 理学院,贵州 毕节 551700
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| 摘要: |
| 提出了概率有限自动机的覆盖的定义,然后利用代数的方法讨论了概率有限自动机的全直积(限制直积)、级联积、圈积、并积的覆盖关系,证明了2个概率有限自动机的级联积(限制直积)覆盖它们的圈积(全直积),概率有限自动机的圈积的全直积覆盖它们的全直积的圈积,给出了概率有限自动机的弱同态与覆盖的关系,研究了概率有限自动机的积的覆盖关系的传递性质. |
| 关键词: 概率有限自动机 积 覆盖 同态 |
| DOI： |
| 分类号:TP301.1 |
| 基金项目:广西自然科学基金资助项目(2014GXNSFBA118018；2016GXNSFBA380165);广西高校复杂系统优化与大数据处理重点实验室开放基金资助项目(2015CSOBDP0104);贵州省科技合作计划资助项目(黔科合LH字［2016］7062号) |
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| On covering of products of probabilistic finite automata |
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Yang Jingkai1,2, Cai Yongyu3, Cheng Yuqiang1, Huang Feidan41,2,3,4
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1. College of Mathematics and Statistics, Yulin Normal University,Yulin 537000,China;2. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Large Data Processing,
Yulin Normal University , Yulin 537000, China;3. College of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China;4. School of Science, Guizhou University of Engineering Science, Bijie 551700, China
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| Abstract: |
| The concept of covering of probabilistic finite automata was introduced, covering relationship on several kinds of products of probabilistic finite automata, such as full direct product(restricted direct product), cascade product, wreath product and join were discussed, it was proved that the cascade product(restricted direct product) of two probabilistic finite automata covered their wreath product(full direct product), full direct product of wreath product of probabilistic finite automata covered their wreath product of full direct product, the relations between weak homomorphism of probabilistic finite automata and covering of probabilistic finite automata were given, transitivity of covering of product of probabilistic finite automata were investigated. |
| Key words: probabilistic finite automata product covering homomorphism |
