摘要
状态机的很多性质在计算机等方面有着广泛的应用,因此对状态机的研究具有重要的意义.本文给出了幺半环上模糊有限状态机的概念,对状态之间的等价进行了定义,引入了同态的概念,得到同态定理和满同态分解定理,讨论了幺半环上模糊有限状态机在同态下的交换性质和连通性以及子状态机的可分离性.
Many properties of state machines have a wide range of application in the areas such as computer etc., so the study to state machines is very significant. In this paper, the notion of fuzzy finite state machines over unitary semirings is given, the equivalence between states of fuzzy finite state machines over unitary semirings is defined, and the notion of homomorphism between two fuzzy finite state machines over unitary semirings is introduced. Homomorphism Theorem and Epimorphism Decomposition Theorem are obtained, and the exchange property, connectivity and separability of submachines of fuzzy finite state machines over unitary semirings under homomorphism are discussed.
出处
《纯粹数学与应用数学》
CSCD
2009年第2期363-371,共9页
Pure and Applied Mathematics
基金
国家自然科学基金(60473005)
广西自然科学基金(0832103
0640061)
关键词
幺半环
状态机
交换性质
连通
分离
同态
unitary semirings, state machines, exchange property, connectivity, separability, homomorphism
