两类循环模糊自动机的弱等价性

定义循环模糊自动机和循环模糊有限状态自动机,并讨论了这两类循环模糊自动机的弱等价性.     

基于二型模糊逻辑的元胞自动机模型

将二型模糊逻辑推理引入到元胞自动机模型中,把二型模糊逻辑推理与经典的元胞自动机模型结合起来,建立一种新的推理演化模型,基于二型模糊逻辑的元胞自动机模型.元胞自动机模型的关键部分是演化规则和元胞状态.将元胞自动机模型中的演化规则二型模糊化,将经典元胞自动机模型中的元胞状态模糊化为二型模糊状态,建立基于二型模糊逻辑的元胞自动机模型.     

通用模糊自动机

首先使用模糊语言的分解定义了通用模糊自动机:这个自动机以该模糊语言的分解作为状态,通过模糊语言的包含度定义其转移函数。其次定义了模糊自动机上的态射,证明了接受给定模糊语言的所有自动机都可以标准地映射到该语言对应的通用模糊自动机上,这个性质称为通用性。最后进一步讨论了模糊商自动机,模糊m-最小自动机,模糊最小自动机及与通用模糊自动机之间的关系。     

循环模糊有限自动机的同态性质

讨论了模糊有限自动机(即模糊Mealy机)的同态性质和循环模糊有限自动机的同态性质,证明了每个模糊有限自动机都是有限个循环模糊有限自动机的直和的同态象。     

模糊自动机的强连通性及群自动机

为了更好地研究模糊自动机的结构和性质,采用代数的方法,在传统的模糊有限状态自动机的基础上,通过定义状态集合为代数群的自动机,讨论了这一类自动机的连通性和正则性,这丰富了模糊自动机理论．     

最小化基于合成模糊变换的模糊自动机

经过重新定义模糊自动机,使得模糊自动机的识别过程与一个合成模糊变换(CF变换)一致,而且得到了尊重合成模糊变换的最粗分类即为状态集的最粗等价分类这一重要结论.在对尊重合成模糊变换的最粗分类的讨论中,给出了找到尊重合成模糊变换的最粗分类的有限步算法,亦即状态集的最粗等价分类和最小化模糊自动机的算法.该算法不仅给出了最长运算时间,而且还给出可终止算法的条件,使得运算更为可行和简便.     

幺半环上模糊有限状态自动机积的覆盖关系

提出了幺半环上模糊有限状态自动机的各种乘积以及覆盖的定义,并得到了一些性质.证明了直积、级联积、圈积三种乘积以及和之间的覆盖关系,得到了乘积自动机、和自动机覆盖关系的一些代数性质.     

模糊剩余自动机

在[0,1]格值区间上引入了模糊剩余自动机(FRFA)的概念:若一个模糊自动机(FFA)的每一个状态都定义了其接受语言的一个剩余语言,则称为模糊剩余自动机.讨论了模糊剩余自动机的一些性质以及模糊自动机的消去与饱和运算.在定义既约模糊剩余语言的基础上定义了标准模糊剩余自动机,并给出了构造方法.证明了一个模糊正则语言对应的标准FRFA即为识别这个语言的最小状态FFA,此研究为模糊自动机的状态最小化研究提供了另一种研究思路.     

模糊有限自动机的kronecker积

在矩阵理论框架下,引入了模糊有限自动机转移矩阵,变换矩阵半群以及覆盖概念.定义了模糊有限自动机Kronecker积,讨论了其转移矩阵性质及变换矩阵半群间的覆盖关系.     

基于格半群的有限状态自动机的同态

本文研究了格值有限状态自动机(LFSA)的同态和强同态及其性质.利用强同态概念,在格值有限状态自动机的状态集上建立了一种等价关系,得到了格值有限状态自动机的商自动机,证明了商自动机与强同态像自动机同构.     

关于 Fuzzyω正则语言的一个注记

通过引入ω-Nerode等价关系,fuzzy前逆缀ω-语言,闭左逆语言等概念来研究语言的化数性质,得到了(1)fuzzyω正则语言可由一些具有有限指标集的等价类来表示;(2)fuzzy前逆缀ω-语言是fuzzyω正则语言iff由L定义的ω-Nerode等价关系的指标集是有限的.     

Fuzzy有理语言与Fuzzy有限态自动机的关系

引入了fuzzy有理语言的概念,得到了∑+的子集可识别当且仅当有理的.从而揭示了fuzzy有理语言与fuzzy有限态自动机语言的关系.     

关于Fuzzy正则语言的一些性质

在定义Fuzzy正则语言,Fuzzy有理语言等的基础上,研究Fuzzy正则语言相关的一些性质,得到Fuzzy正则语言与Fuzzy有理语言间的对应关系,对Fuzzy有限状态自动机的简化具有应用价值。     

On the complexity of the word problem for automaton semigroups and automaton groups

In this paper, we study the word problem for automaton semigroups and automaton groups from a complexity point of view. As an intermediate concept between automaton semigroups and automaton groups, we introduce automaton-inverse semigroups, which are generated by partial, yet invertible automata. We show that there is an automaton-inverse semigroup and, thus, an automaton semigroup with a PSpace-complete word problem. We also show that there is an automaton group for which the word problem with a single rational constraint is PSpace-complete. Additionally, we provide simpler constructions for the uniform word problems of these classes. For the uniform word problem for automaton groups (without rational constraints), we show NL-hardness. Finally, we investigate a question asked by Cain about a better upper bound for the length of a word on which two distinct elements of an automaton semigroup must act differently.A detailed listing of the contributions of this paper can be found at the end of this paper.     

The Lamplighter Group ℤ3≀ℤ Generated by a Bireversible Automaton

We construct a bireversible self-dual automaton with three states over an alphabet with three letters which generates the lamplighter group ?₃??. In particular, this fact shows that not all groups defined by birevirsible automata are finitely presented.     

On minimal realization of fuzzy behaviour and associated categories

This paper is towards the study of minimal deterministic automata with fuzzy output which realizes the given fuzzy behaviour. The construction of such automaton is based on Myhill-Nerode’s theory, and it is shown that this automaton is a canonical realization of given fuzzy behaviour. Meanwhile, we introduce the categories of deterministic automata with fuzzy output and fuzzy behaviour. The relationship between both the categories through functors is also studied.     

具有输出字符功能的模糊自动机的最小化问题

通过文献[8]中两类具有输出字符功能的Fuzzy自动机和Fuzzy有限状态自动机的强等价性,等价性和弱等价性的条件,在以往仅仅给出的Fuzzy有限状态自动机的最小化问题基础上,讨论了具有更广泛意义的具有输出字符功能的Fuzzy自动机的最小化问题,以及其最小化自动机与Fuzzy有限状态自动机的最小化自动机在不同条件下的关系。     

Evaluation of fully fuzzy matrix equations by fuzzy neural network

In this paper, a new hybrid method based on fuzzy neural network for approximate solution of fully fuzzy matrix equations of the form AX=D$\mathit{AX}=D$, where A and D are two fuzzy number matrices and the unknown matrix X is a fuzzy number matrix, is presented. Then, we propose some definitions which are fuzzy zero number, fuzzy one number and fuzzy identity matrix. Based on these definitions, direct computation of fuzzy inverse matrix is done using fuzzy matrix equations and fuzzy neural network. It is noted that the uniqueness of the calculated fuzzy inverse matrix is not guaranteed. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate solution of fuzzy matrix equations that supposedly has a unique fuzzy solution, a simple algorithm from the cost function of the fuzzy neural network is proposed. To illustrate the easy application of the proposed method, numerical examples are given and the obtained results are discussed.     

Fuzzy正则表达式与Fuzzy有限态自动机的关系

首先给出了Fuzzy正则表达式的定义,接着通过研究Fuzzy正则表达式与Fuzzy有限态自动机的关系,得到了两个重要性质,即：每一个Fuzzy正则表达式,都有一个非确定性的Fuzzy有限态自动机接受其代表的语言;每一个被确定性的Fuzzy有限态自动机接受的语言,都能被一个Fuzzy正则表达式表示．     

Evaluation of fuzzy regression models by fuzzy neural network

In this paper, a novel hybrid method based on fuzzy neural network for approximate fuzzy coefficients (parameters) of fuzzy linear and nonlinear regression models with fuzzy output and crisp inputs, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate parameters, a simple algorithm from the cost function of the fuzzy neural network is proposed. Finally, we illustrate our approach by some numerical examples.