Tree-stack automata

We introduce a new model of stack automata, the “tree-stack automata,” extending the linear stack to a tree-stack. A main subject of our investigations is to explore the relationship between tree-stack automata and stack automata. The main result of this paper is that tree-stack have the same recognition power as stack-pushdown automata, another (well-known) extension of stack automata. Therefore we obtain that the class of languages accepted by the one-way (linear) stack automata is a proper subset of the class of languages accepted by the one-way tree-stack automata and that two-way tree-stack automata have the same recognition power as two-way (linear) stack automata. As a special case of tree-stack automata we consider tree-pushdown automata. As opposed to stack automata the tree-pushdown storage does not extend the recognition power of one-way (resp. two-way) pushdown automata.     

Marker automata

This paper deals with finite automata augmented with markers which the automata can move about on their input tapes. The concept of augmenting markers to automata was first introduced by Blum and Hewitt [1] in two-dimensional automata. Kreider, Ritchie, and Springsteel [6, 7, 8, 12] investigated recognition of context-free languages by (one-dimensional) automata with markers. In this paper, we investigate some fundamental properties of marker automata and study their relationships to other types of automata and languages. The main result in this paper is the establishment of an infinite hierarchy of languages recognizable by deterministic and deterministic, halting marker automata. It also turns out that, because of the equivalence of finite marker automata and multi-head automata, the study of three-marker automata becomes very interesting due to results of Hartmanis [4] and Savitch [10].     

Asynchronous cellular learning automata

Cellular learning automata is a combination of cellular automata and learning automata. The synchronous version of cellular learning automata in which all learning automata in different cells are activated synchronously, has found many applications. In some applications a type of cellular learning automata in which learning automata in different cells are activated asynchronously (asynchronous cellular learning automata) is needed. In this paper, we introduce asynchronous cellular learning automata and study its steady state behavior. Then an application of this new model to cellular networks has been presented.     

Finite automata theory with membership values in lattices

In this paper, we study finite automata with membership values in a lattice, which are called lattice-valued finite automata. The extended subset construction of lattice-valued finite automata is introduced, then the equivalences between lattice-valued finite automata, lattice-valued deterministic finite automata and lattice-valued finite automata with ε-moves are proved. A simple characterization of lattice-valued languages recognized by lattice-valued finite automata is given, then it is proved that the Kleene theorem holds in the frame of lattice-setting. A minimization algorithm of lattice-valued deterministic finite automata is presented. In particular, the role of the distributive law for the truth valued domain of finite automata is analyzed: the distributive law is not necessary to many constructions of lattice-valued finite automata, but it indeed provides some convenience in simply processing lattice-valued finite automata.     

Sand automata as cellular automata

In this paper, we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space. This relation induces a compact topology for sand automata, and a new context in which sand automata are homeomorphic to cellular automata acting on a specific subshift. We show that the existing topological results for sand automata, including the Hedlund-like representation theorem, still hold. In this context, we give a characterization of cellular automata which are sand automata, and study some dynamical behaviors such as equicontinuity. Furthermore, we deal with simple sand automata. We show that the classical definition of nilpotency is not meaningful for sand automata. Then, we introduce the suitable new notion of flattening sand automata. Finally, we prove that this simple dynamical behavior is undecidable.     

格值交替树自动机

交替（树）自动机因其本身关于取补运算的简洁性及其与非确定型（树）自动机的等价性,成为自动机与模型检测领域研究的一个新方向.在格值交替自动机与经典交替树自动机概念的基础上,引入格值交替树自动机的概念,并研究了格值交替树自动机的代数封闭性和表达能力.首先,证明了对格值交替树自动机的转移函数取对偶运算,终止权重取补之后所得自动机与原自动机接受语言互补这一结论.其次,证明了格值交替树自动机关于交、并运算的封闭性.最后,讨论了格值交替树自动机和格值树自动机、格值非确定型自动机的表达能力;证明了格值交替树自动机与格值树自动机的等价性,并给出了二者相互转化的算法及其复杂度分析;同时,提供了用格值非确定型自动机来模拟格值交替树自动机的方法.     

接口自动机--一种用于组件组合的形式系统

接口自动机是描述基于组件系统中组件及组件间交互行为的形式化工具。接口自动机在处理组件组合问题时所使用的“乐观方法”和博弈思想是区别于其它形式化工具的关键点。本文对接口自动机、时间接口自动机和资源接口及其中的博弈思想进行综述。在同其它形式化方法比较的基础上,指出了接口自动机的长处和局限。文中总结了接口自动机在理论上和实际中的意义并对其应用前景做了展望。     

自动机与模型检查

首先介绍自动机识别有限词和无限词两种情况,然后结合模型检查方法,把自动机作为规范自动机与模型自动机,使用自动机识别语言的包含问题技巧来解决模型检查问题,这里强调的是Vardi与Wolper提出的方法。     

几类带空转移的n元伪加权自动机的关系

引入了n元伪加权有穷自动机——带有n个有限字符集的伪加权有穷自动机、分明型n元伪加权有穷自动机和确定型n元伪加权有穷自动机的概念。根据状态转移函数在每个字符集上是否带空转移, 将以上自动机分为4类:带r-型空转移的n元伪加权有穷自动机和带空转移的n元伪加权有穷自动机和带r-型空转移的分明型n元伪加权有穷自动机和带空转移的分明型n元伪加权有穷自动机。给出了以上自动机所识别语言的定义并探究了它们之间的关系,讨论了状态转移函数在每个字符集上是否带空转移对其接受语言的影响。     

Structure of weakly invertible semi-input-memory finite automata with delay 2

Semi-input-memory finite automata,a kind of finite automata introduced by the author of this paper for studying error propagation,are a generalization of input-memory finite automata by appending an autonomous finite automaton component.This paper gives a characterization on the structure of weakly invertible semi-input-memory finite automata with delay 2 in which input alphabets and output alphabets have two elements and autonomous finite automata are cyclic.For the structure of feedforward inverse finite automata with delay 2,Zhu first gave a characterization;from a result on mutual invertibility of finite automata,the result mentioned above also leads to a different characterization on the structure of feedforward result mentioned above also leads to a different characterization on the structure of feedforward inverse finite automata with delay 2.     

模糊有限自动机的最小化算法优化

现有的模糊自动机最小化算法没有涉及到对模糊自动机状态的隶属度迁移和变化的讨论,优化的模糊自动机最小化算法弥补了这类算法的不足之处。该算法将模糊有限自动机首先转化为单个初始状态的模糊自动机,然后再将转化后的模糊自动机化简为最小模糊自动机,算法在转化过程中单独讨论了模糊自动机状态隶属度的转化方式,使得算法更加严谨和简化。     

A Kleene–Schützenberger theorem for weighted timed automata

During the last years, weighted timed automata have received much interest in the real-time community. Weighted timed automata form an extension of timed automata and allow us to assign weights (costs) to both locations and edges. This model, introduced by Alur et al. (2001) and Behrmann et al. (2001), permits the treatment of continuous consumption of resources and has led to much research on scheduling problems, optimal reachability and model checking. Also, several authors have derived Kleene-type characterizations of (unweighted) timed automata and their accepted timed languages. The goal of this paper is to provide a characterization of the behaviours of weighted timed automata by rational power series. We define weighted timed automata with weights taken in an arbitrary semiring, resulting in a model that subsumes several weighted timed automata concepts of the literature. For our main result, we combine the methods of Schützenberger, a recent approach for a Kleene-type theorem for unweighted timed automata by Bouyer and Petit as well as new techniques. Our main result also implies Kleene-type theorems for several subclasses of weighted timed automata investigated before, e.g., for timed automata and timed automata with stopwatch observers.     

线性有限自动机的同步序列及其生成算法

文章主要讨论了线性有限自动机的同步序列,得到了线性有限自动机有同步序列的充要条件,还讨论了一类输入存贮线性有限自动机及可等价嵌入输入存贮线性有限自动机的极小线性有限自动机的同步序列。最后给出了判断线性有限自动机有无同步序列以及求线性有限自动机(最短)同步序列的一些算法。     

量子自动机的刻画

澄清了各类量子自动机之间的相互关系,并给出了量子自动机的各种等价刻画定理.引入G-量子自动机、g-量子自动机、(广义)量子自动机及G-量子文法和g-量子文法,并阐明了它们与其他量子自动机之间的等价关系.在一定条件下讨论了G(g)-量子自动机与G(g)-量子文法的等价性,从而解决了关于量子文法产生量子正规语言的问题.讨论了量子语言与正规语言的关系,特别是回答了Gudder提出的两个公开问题.最后,给出了一种减少状态空间维数的方法.     

弱可逆线性有限自动机的一种分解

讨论有限自动机的分解有助于分析弱可逆有限自动机的结构和求解弱逆.首先证明了弱同构的弱可逆有限自动机具有相似的分解形式;接着考虑了一类特殊的弱可逆线性有限自动机的分解,从状态输出权的角度刻画了该分解存在的一个充分条件;然后把这种分解形式推广到了一般的弱可逆线性有限自动机上,即:延迟τ步弱可逆线性有限自动机分解成延迟0步弱可逆有限自动机和一种特殊的有限自动机MD,并得到了分解存在的充要条件;最后,用输出序列的代数性质来刻画其中的充分条件,并把它转化成了一个矩阵的秩的计算.这种分解形式并不局限于n元弱可逆有限自动机,而且分解条件也比较简单,仅与输出序列的性质有关.     

扰动值模糊有限自动机及其语言*

引入扰动值模糊有限自动机及其语言的概念,讨论扰动值模糊有限自动机的状态转移函数的扩张问题,证明3类确定型扰动值模糊有限自动机、非确定型扰动值模糊有限自动机相互等价性,研究扰动值模糊有限自动机的语言关于正则运算的封闭性.     

确定型模糊多重集有限自动机的极小化

主要研究确定型模糊多重集有限自动机的状态极小化问题。给出了模糊多重集有限自动机的同余和同态概念,并利用同余和同态关系研究了确定型模糊多重集有限自动机的极小化问题。进一步从确定型模糊多重集有限自动机自身出发,构造出极小模糊多重集有限自动机,并给出了极小化的算法。     

Improved constructions of mixed state quantum automata

Quantum finite automata with mixed states are proved to be super-exponentially more concise rather than quantum finite automata with pure states. It was proved earlier by A. Ambainis and R. Freivalds that quantum finite automata with pure states can have an exponentially smaller number of states than deterministic finite automata recognizing the same language. There was an unpublished “folk theorem” proving that quantum finite automata with mixed states are no more super-exponentially more concise than deterministic finite automata. It was not known whether the super-exponential advantage of quantum automata is really achievable.     

量子自动机的交换性

定义了量子自动机及广义量子自动机的交换性,并提出了（广义）量子自动机所识别语言的交换性。利用半群及矩阵研究（广义）量子自动机的交换性,得出了（广义）量子自动机交换性的几个等价刻画。研究了（广义）量子自动机的交换性与其所识别语言的交换性的关系,证明了交换的（广义）量子自动机所识别的语言也是交换的。此外,讨论了（广义）量子自动机的广义直积、全直积、限制直积、级联积和圈积等积的交换性,得出了一些积的交换性的充分条件和必要条件。     

An overview of quantum computation models: quantum automata

Quantum automata, as theoretical models of quantum computers, include quantum finite automata (QFA), quantum sequential machines (QSM), quantum pushdown automata (QPDA), quantum Turing machines (QTM), quantum cellular automata (QCA), and the others, for example, automata theory based on quantum logic (orthomodular lattice-valued automata). In this paper, we try to outline a basic progress in the research on these models, focusing on QFA, QSM, QPDA, QTM, and orthomodular lattice-valued automata. Also, other models closely relative to them are mentioned. In particular, based on the existing results in the literature, we finally address a number of problems to be studied in future.