模糊有穷自动机的互模拟关系

Bisimulation Relations for Fuzzy Finite Automata

互模拟是离散事件系统中的一个等价关系,它已经应用到概率、随机和加权自动机中。本文给出模糊有穷自动机(FFA)前向互模拟关系和后向互模拟关系的定义,并给出它们的一些性质,证明前向和后向互模拟关系对于模糊有穷自动机(FFA)的一些运算(并,连接,交)和模糊正则语言的表现定理是封闭的。另外文中还给出一个可在有限步计算极大前向互模拟关系的算法,最后指出前向和后向互模拟之间的区别。

Bisimulation is a well known equivalence relation for discrete event systems and hasbeen extended to probabilistic, stochastic and weighted automata. This paper introduces definitions of forward and backward bisimulation which can be applied to FFA. Some properties of them are introducedand it is shown that some commonly known compositions （union, connection, intersection） and representation theorem of fuzzy regular language for FFA are closed under bisimulation. This paper also introduces a algorithm to compute largest forward bisimulation. In theend, the difference between forward bisimulation and backward bisimulation is given.