有限自动机可识别语言的基数

利用有向图的邻接矩阵研究有限自动机的可识别语言的基数问题。通过建立有限自动机的可识别语言与其有向图中从初始结点（有限自动机的初始状态）到终止结点（有限自动机的终止状态）的路的一一对应关系,利用邻接矩阵给出了有限自动机的可识别语言的基数公式,研究了两个自动机不等价的充分条件。     

Irredundant Algorithms for Traversing Directed Graphs: The Deterministic Case

Problems of testing program systems modeled by deterministic finite automata are considered. The necessary (and, sometimes, sufficient) component of such testing is a traversal of the graph of the automaton state transitions. The main attention is given to the so-called irredundant traversal algorithms (algorithms for traversing unknown graphs, or on-line algorithms), which do not require an a priori knowledge of the total graph structure.     

Recognition of directed acyclic graphs by spanning tree automata

In this paper, we study tree automata for directed acyclic graphs (DAGs). We define the movement of a tree automaton on a DAG so that a DAG is accepted by a tree automaton if and only if the DAG has a spanning tree accepted by the tree automaton. We call this automaton a spanning tree automaton. The NP-completeness of the membership problem of DAGs for spanning tree automata is shown. However, if inputs are restricted to series–parallel graphs or generalized series–parallel graphs, it is shown that the membership problem for spanning tree automata is solvable in linear time.     

有限自动机在复合事件检测中的应用

针对早期系统只提供原子事件的检测机制,不能检测由原子事件组成的复合事件的问题,提出了用有限自动机来检测复合事件的方法.说明了复合事件的组成和表达式,利用自动机原理对复合事件的检测模式进行了分析,给出了复合事件检测的具体过程:从事件表达式到不确定的有限自动机,从不确定的有限自动机到最小化确定的有限自动机,再用程序实现了确定的有限自动机.实例表明,自动机模型是检测复合事件的一种有效实现方式.     

自动机到正规表达式的重构方法研究

自动机理论是编译程序中单词识别的基本理论。论文分析了自动机与正规表达式等价性定理,指出了从确定有限自动机到正规表达式重构规则中存在的问题,给出了一个包含多个结点所组成回路的有限自动机到正规表达式的重构定理,并通过实例对于该定理所阐明的方法的运用进行了详细的讨论。     

On finite automata with limited nondeterminism

We develop a new algorithm for determining if a given nondeterministic finite automaton is limited in nondeterminism. From this, we show that the number of nondeterministic moves of a finite automaton, if limited, is bounded by where is the number of states. If the finite automaton is over a one-letter alphabet, using Gohon's result the number of nondeterministic moves, if limited, is less than . In both cases, we present families of finite automata demonstrating that the upper bounds obtained are almost tight. We also show that the limitedness problem of the number of nondeterministic moves of finite automata is PSPACE-hard. Since the problem is already known to be in PSPACE, it is therefore PSPACE-complete. Received: 14 June 1994 / 3 December 1997     

Reachability Problems on Regular Ground Tree Rewriting Graphs

We consider the transition graphs of regular ground tree (or term) rewriting systems. The vertex set of such a graph is a (possibly infinite) set of trees. Thus, with a finite tree automaton one can represent a regular set of vertices. It is known that the backward closure of sets of vertices under the rewriting relation preserves regularity, i.e., for a regular set T of vertices the set of vertices from which one can reach T can be accepted by a tree automaton. The main contribution of this paper is to lift this result to the recurrence problem, i.e., we show that the set of vertices from which one can reach infinitely often a regular set T is regular, too. Since this result is effective, it implies that the problem whether, given a tree t and a regular set T, there is a path starting in t that infinitely often reaches T, is decidable. Furthermore, it is shown that the problems whether all paths starting in t eventually (respectively, infinitely often) reach T, are undecidable. Based on the decidability result we define a fragment of temporal logic with a decidable model-checking problem for the class of regular ground tree rewriting graphs.     

Fuzzy automaton finite state recognition

The fuzzy automaton finite state recognition problem is investigated. We introduced a generalized definition of a homing sequence for fuzzy automaton (FA). The investigated problem for FA belongs to the class of multicriteria problems, which distinguishes it from the analogous problem for classical finite state automatons. Algorithms for constructing generalized homing sequences that are optimal according to various criteria are proposed.     

哈密顿路径问题的一种基于有穷自动机的DNA算法

提出了一种基于有穷自动机的解决哈密顿路径问题的DNA算法,将有穷自动机的状态用含有DNA限制性内切酶的识别位点的DNA双链分子来编码,通过限制性内切酶的生物化学反应来实现状态的转移。算法的创新之处在于用DNA计算模拟有穷自动机的运行过程中,保留了其经过的各个状态,以便最后筛选出经过各个顶点的路径。算法的优点是实验实现简易,大大减少所使用的DNA分子的数量。     

Finite time analysis of the pursuit algorithm for learning automata

The problem of analyzing the finite time behavior of learning automata is considered. This problem involves the finite time analysis of the learning algorithm used by the learning automaton and is important in determining the rate of convergence of the automaton. In this paper, a general framework for analyzing the finite time behavior of the automaton learning algorithms is proposed. Using this framework, the finite time analysis of the Pursuit Algorithm is presented. We have considered both continuous and discretized forms of the pursuit algorithm. Based on the results of the analysis, we compare the rates of convergence of these two versions of the pursuit algorithm. At the end of the paper, we also compare our framework with that of Probably Approximately Correct (PAC) learning.     

An algorithmic method for increasing ADC fault resilience

A method for the transformation of algorithms of the operation of sequential ADCs into algorithms correcting faults in the discrete part of an ADC is presented. A graphical method for the determination of the operation conditions of discrete control devices (finite automata) of ADCs resilient to single-event upsets is applied. The properties of the behavior of a graph of a finite automaton for which the ADC realizes noise-immune approximation algorithms are formulated. Procedures for the construction of such graphs are presented.     

一种基于时间自动机的域构造方法

模型检验是一种重要的形式化自动验证技术,通过状态空间搜索来保证软硬件设计的正确性。由于TCTL不是针对时间自动机,而是针对有限状态变迁系统的,从而无法使用TCTL直接对时间自动机进行模型检验。给出了一种从时间自动机到有限状态变迁系统的方法,并在不改变时间自动机的语义上,使时间自动机等价后的域状态数尽可能少,在一定程度上有效地解决了状态空间爆炸问题。     

一种基于编码关联的快速多模式匹配算法

多模式匹配算法经常使用有限自动状态机来实现多个模式串的并行匹配。针对基于自动状态机的多模式匹配算法在应用于中文编码时存在的存储空间膨胀问题,使用中文字符的拆分编码构造自动状态机,以优化算法自动状态机的存储空间,并利用中文编码的编码关联性,设计了一种基于编码关联跳转的失效跳转表,使用启发式跳跃规则提升匹配算法的时间性能。最后通过实验证明,中文编码环境下,相比于其它使用自动状态机的多模式匹配算法,改良算法拥有更小的空间消耗与更快的运行速度。     

Compositional entailment checking for a fragment of separation logic

We present a decision procedure for checking entailment between separation logic formulas with inductive predicates specifying complex data structures corresponding to finite nesting of various kinds of singly linked lists: acyclic or cyclic, nested lists, skip lists, etc. The decision procedure is compositional in the sense that it reduces the problem of checking entailment between two arbitrary formulas to the problem of checking entailment between a formula and an atom. Subsequently, in case the atom is a predicate, we reduce the entailment to testing membership of a tree derived from the formula in the language of a tree automaton derived from the predicate. The procedure is later also extended to doubly linked lists. We implemented this decision procedure and tested it successfully on verification conditions obtained from programs using both singly and doubly linked nested lists as well as skip lists.     

Deterministic finite automata representation for model predictive control of hybrid systems

As is well known, the computational complexity in the mixed integer programming (MIP) problem is one of the main issues in model predictive control (MPC) of hybrid systems such as mixed logical dynamical systems. Thus several efficient MIP solvers such as multi-parametric MIP solvers have been extensively developed to cope with this problem. On the other hand, as an alternative approach to this issue, this paper addresses how a deterministic finite automaton, which is a part of a hybrid system, should be expressed to efficiently solve the MIP problem to which the MPC problem is reduced. More specifically, a modeling method to represent a deterministic finite automaton in the form of a linear state equation with a smaller set of binary input variables and binary linear inequalities is proposed. After a motivating example is described, a derivation procedure of a linear state equation with linear inequalities representing a deterministic finite automaton is proposed as three steps; modeling via an implicit system, coordinate transformation to a linear state equation, and state feedback binarization. Various significant properties on the proposed modeling are also presented throughout the proofs on the derivation procedure.     

基于CNN与有限状态自动机的手写体大写金额识别

手写票据识别是模式识别中的研究难点之一,手写体风格多样、票据背景复杂等原因导致手写票据识别的准确率不高。大写金额作为票据中最重要的部分,对其进行准确识别是手写票据自动识别的关键。对基于分割的手写体大写金额识别及处理问题进行研究,提出一种基于卷积神经网络（CNN）与有限状态自动机的手写体大写金额识别方法。在利用过分割和组合过分割项得到单字符后使用CNN对其进行识别。通过对字符进行分类、定义各类字符之间的逻辑关系构造用于语法检查的有限状态自动机,通过语法自动机在识别结果中选择符合语法规则的字符串,并在路径搜索中利用语法自动机优化搜索性能。在此基础上,运用语法自动机对模糊字符进行预测,以纠正CNN的识别错误。实验结果表明,该方法在对大写金额单字符和文本行进行识别时准确率分别高达98.2%与96.6%。     

一种测试语言包含的算法

在积自动机基础上,利用互模拟关系引出商自动机,用以解决积自动机的状态组合爆炸问题。进而提出一个自然的测试语言包含的算法,这种算法的空间复杂度与规范自动机的状态目呈指数关系即O（2^k),其中K是规范自动机的状态数目。     

Efficient recognition of trace languages defined by repeat-until loops

A sequence of operations may be validly reordered, provided that only pairs of independent operations are commuted. Focusing on a program scheme, idealized as a local finite automaton, we consider the problem of checking whether a given string is a valid permutation of a word recognized by the automaton. Within the framework of trace theory, this is the membership problem for rational trace languages. Existing general algorithms, although time-polynomial, have unbounded degree related to some properties of the dependence graph. Here we present two original linear-time solutions. A straightforward algorithm is suitable for any finite automaton such that all the transitions starting from the same state are labelled by dependent symbols. The second approach is currently restricted to automata representing programs of nested repeat-until loops. Using integer compositions to represent loop iterations and under suitable conditions, the algorithm constructs the syntax tree of a possible word equivalent to the input string. The same procedures show that, under our hypotheses, the uniform version of the membership problem (which is NP-complete in the general case) is solvable in polynomial time.     

Blocking of group automata. II. Mutual interlocking

Groups of automata formed by mutually interlocking connections of permutation automata are considered. Groups of maximal mutually interlocking connections of any permutation automata are found. The notion of simulation of a finite automaton by a semigroup of transactions of another automaton is introduced. An algorithm for construction of the model of finite permutation automaton using mutually interlocking connections of permutation triggers is given.