赋权型自动机的不同模型研究

自动机理论是理论计算机科学的基础理论之一,在很多领域自动机有着广泛的应用,有穷状态自动机是正则语言的识别机器,通常分为确定型与非确定型两种模型,其识别语言的能力是等价的。赋权自动机是另一类重要的自动机模型,自动机的每条转移规则和状态可以赋以某一代数结构上的某一数值,从而可以计算输入字符串的权值。任何有穷状态自动机都可以视为一特殊赋权自动机,因此赋权自动机功能更强大,应用更为广泛。     

Controlled finite automata

This paper discusses finite automata regulated by control languages over their states and transition rules. It proves that under both regulations, regular-controlled finite automata and context-free-controlled finite automata characterize the family of regular languages and the family of context-free languages, respectively. It also establishes conditions under which any state-controlled finite automaton can be turned into an equivalent transition-controlled finite automaton and vice versa. The paper also demonstrates a close relation between these automata and programmed grammars. Indeed, it proves that finite automata controlled by languages generated by propagating programmed grammars with appearance checking are computationally complete. In fact, it demonstrates that this computational completeness holds even in terms of these automata with a reduced number of states.     

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。     

通过单向队列自动机对适应性移动计算系统中组合事件的分析

近年来,移动计算吸引着越来越多的注意力.适应性移动计算系统要求大范围的事件组合,这些事件包括逻辑事件、时间事件和暂时事件等.致力于组合事件和组合反应的设计和实现,考虑了事件流、时间事件和不同操作符等情况.组合事件的检测由一种新的扩展自动机??单向队列自动机来有效地支持,详细定义和讨论了单向队列自动机,并具体描述了使用它来检测组合事件的机制和所使用的数据结构.     

Checking Temporal Duration Properties of Timed Automata

In this paper, the problem of checking a timed automaton for a Duration Calculus formula of the form Temporal Duration Property is addressed. It is shown that Temporal Duration Properties are in the class of discretisable real-time properties of Timed Automata, and an algorithm is given to solve the problem based on linear programming techniques and the depth-first search method in the integral region graph of the automaton. The complexity of the algorithm is in the same class as that of the solution of the reachability problem of timed automata.     

加权迁移系统线性时间属性及其安全性检测

针对加权迁移系统,提出了线性时间属性及其安全性检测。首先定义了半环K上的加权迁移系统,提出了加权线性时间属性概念,并根据权重函数确定加权线性时间属性的上确界、下确界和闭包; 接着给出了几种常见的加权线性时间属性并且讨论了它们的关系; 然后重点研究了加权安全性,通过加权自动机和闭包给出了加权正则安全性; 最后基于加权有穷自动机,建立了加权正则安全性的检测方法。检测过程结合半环和形式幂级数,构造了加权迁移系统和加权有穷自动机的乘积系统,将加权安全性检测问题转化为验证乘积系统的不变性,给出了加权正则安全性检测的算法和复杂度。实例结果表明,所提的方法能够对加权迁移系统的安全性进行检测。     

UML Statecharts的模型检验方法

统一建模语言UML已广泛应用于软件开发中,验证UML模型是否满足某些关键性质成为一个重要问题.提出了对UML Statecharts进行模型检验的方法.首先用扩展层次自动机结构化地表示UML Statecharts,然后给出其操作语义,通过寻找最大无冲突迁移集可以保证语义的正确性.对于具有无穷运行的系统,该操作语义可以映射到一个Büchi自动机.使用基于自动机理论的模型检验方法来验证UML Statecharts的线性时态逻辑性质,并给出方法验证由Statecharts和协同图建模的复杂多对象系统.     

La representation ergodique d'un automate fini

We study a special class of finite automata called reversible and defined by the following property: there exists a state such that, starting from it, both the automation and its (deterministic) reversal are strongly connected.The main tool to handle these automata is the ergodic representation which is mainly the Schützenberger matrix representation of the semigroup of the automaton over its minimal ideal. This representation allows the construction of a class of reversible automata: the so called homogeneous ones. This class is precisely the one obtained by considering a class of finite languages that are both prefix and suffix. We obtain here, by means of their automaton, a construction of these languages.     

A monotone framework for CCS

The calculus of communicating systems, CCS, was introduced by Robin Milner as a calculus for modelling concurrent systems. Subsequently several techniques have been developed for analysing such models in order to get further insight into their dynamic behaviour.In this paper we present a static analysis for approximating the control structure embedded within the models. We formulate the analysis as an instance of a monotone framework and thus draw on techniques that often are associated with the efficient implementation of classical imperative programming languages.We show how to construct a finite automaton that faithfully captures the control structure of a CCS model. Each state in the automaton records a multiset of the enabled actions and appropriate transfer functions are developed for transforming one state into another. A classical worklist algorithm governs the overall construction of the automaton and its termination is ensured using techniques from abstract interpretation.     

Efficient inclusion testing for simple classes of unambiguous ω-automata

We show that language inclusion for languages of infinite words defined by nondeterministic automata can be tested in polynomial time if the automata are unambiguous and have simple acceptance conditions, namely safety or reachability conditions. An automaton with safety condition accepts an infinite word if there is a run that never visits a forbidden state, and an automaton with reachability condition accepts an infinite word if there is a run that visits an accepting state at least once.     

正则语言的一个特征

Myhill-Nerode定理利用等价关系描述了正则语言的一个重要特征,它是有限自动机理论中的一个经典、优美的结果。为了将Myhill-Nerode定理推广到更一般的情形,引入了有限自动机M上的状态转移半群和Σ*上的M-半群,讨论了其若干性质。在此基础上,将Myhill-Nerode定理中的等价关系一般化,给出了正则语言的一个新的特征定理,Myhill-Nerode定理成为该定理的一个推论。讨论了正则语言的最一般的特征,提出了有待进一步研究的问题。     

Syntactic reductions for efficient deadlock analysis

A well‐known problem in the verification of concurrent systems based on model checking is state explosion: concurrent systems are often represented by automata with a prohibitive number of states. A reduction technique to reduce state explosion in deadlock checking is presented. The method is based on an automatic syntactic simplification of a calculus of communicating systems (CCS) specification, which keeps the parts of the program structure that may lead to a deadlock and deletes the other parts. Copyright © 2002 John Wiley & Sons, Ltd.     

Don’t care words with an application to the automata-based approach for real addition

Automata have proved to be a useful tool in infinite-state model checking, since they can represent infinite sets of integers and reals. However, analogous to the use of binary decision diagrams (bdds) to represent finite sets, the sizes of the automata are an obstacle in the automata-based set representation. In this article, we generalize the notion of “don’t cares” for bdds to word languages as a means to reduce the automata sizes. We show that the minimal weak deterministic Büchi automaton (wdba) with respect to a given don’t care set, under certain restrictions, is uniquely determined and can be efficiently constructed. We apply don’t cares to improve the efficiency of a decision procedure for the first-order logic over the mixed linear arithmetic over the integers and the reals based on wdbas.     

使用事件自动机规约的C语言有界模型检测

提出使用事件自动机对 C 程序的安全属性进行规约,并给出了基于有界模型检测的形式化验证方法。事件自动机可以规约程序中基于事件的安全属性,且可以描述无限状态的安全属性。事件自动机将属性规约与C程序本身隔离,不会改变程序的结构。在事件自动机的基础上,提出了自动机可达树的概念。结合自动机可达树和有界模型检测技术,给出将事件自动机和C程序转化为可满足性模理论SMT(satisfiability modulo theory)模型的算法。最后,使用SMT求解器对生成的SMT模型求解,并根据求解结果给出反例路径分析算法。实例分析和实验结果表明,该方法可以有效验证软件系统中针对事件的属性规约。     

Succinct representation of regular languages by boolean automata

Boolean automata are a generalization of finite automata in the sense that the ‘next state’, i.e. the result of the transition function given a state and a letter, is not just a single state (deterministic automata) or a union of states (nondeterministic automata) but a boolean function of states. Boolean automata accept precisely regular languages; furthermore they correspond in a natural way to certain language equations as well as to sequential networks. We investigate the succinctness of representing regular languages by boolean automata. In particular, we show that for every deterministic automaton A with m states there exists a boolean automaton with [log₂m] states which accepts the reverse of the language accepted by A (m≥1). We also show that for every n≥1 there exists a boolean automation with n states such that the smallest deterministic automaton accepting the same language has 2⁽²ⁿ⁾ states; moreover this holds for an alphabet with only two letters.     

Timed Automata Patterns

Timed Automata have proven to be useful for specification and verification of real-time systems. System design using Timed Automata relies on explicit manipulation of clock variables. A number of automated analyzers for Timed Automata have been developed. However, Timed Automata lack of composable patterns for high-level system design. Logic-based specification languages like Timed CSP and TCOZ are well suited for presenting compositional models of complex real-time systems. In this work, we define a set of composable Timed Automata patterns based on hierarchical constructs in timed enriched process algebras. The patterns facilitate hierarchical design of complex systems using Timed Automata. They also allow a systematic translation from Timed CSP/TCOZ models to Timed Automata so that analyzers for Timed Automata can be used to reason about TCOZ models. A prototype has been developed to support system design using Timed Automata patterns or, if given a TCOZ specification, to automate the translation from TCOZ to Timed Automata.     

On stateless deterministic restarting automata

The transitions of a stateless automaton do not depend on internal states but solely on the symbols currently scanned by its head accessing the input and memory. We investigate stateless deterministic restarting automata that, after executing a rewrite step, continue to read their tape before performing a restart. Even the weakest class thus obtained contains the regular languages properly. The relations between different classes of stateless automata as well as between stateless automata and the corresponding types of automata with states are investigated, and it is shown that the language classes defined by the various types of deterministic stateless restarting automata without auxiliary symbols are anti-AFLs that are not even closed under reversal.     

A complete characterization of deterministic regular liveness properties

Many systems can be modeled formally by nondeterministic Büchi-automata. The complexity of model checking then essentially depends on deciding subset conditions on languages that are recognizable by these automata and that represent the system behavior and the desired properties of the system. The involved complementation process may lead to an exponential blow-up in the size of the automata. We investigate a rich subclass of properties, called deterministic regular liveness properties, for which complementation at most doubles the automaton size if the properties are represented by deterministic Büchi-automata. In this paper, we will present a decomposition theorem for this language class that entails a complete characterization of the deterministic regular liveness properties, and extend an existing incomplete result which then, too, characterizes the deterministic regular liveness properties completely.     

Interacting automata

Compatibility of interacting partial nondeterministic automata is defined. Two interacting automata are compatible if an input signal from one automaton always induces a defined transition in the other automaton.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 17–29, November–December, 1991.     

LDPChecker一个实时和混成系统模型检验工具

混成系统是一类复杂系统,线性混成系统作为其重要子类,在形式方法中,人们通常使用线性混成自动机来对它建模．虽然线性混成自动机的模型检验问题总的来说还是不可判定的,但对于其中的正环闭合自动机．其对于线性时段性质的满足性能够通过线性规划方法加以检验．为了实现自动检验正环闭合自动机对线性时段性质的满足性,设计并实现了工具LDPChecker．工具LDPChecker能够识别正环闭合自动机并对其进行相应的检验,其主要特色在于它能够对实时和混成系统检验包含可达性在内的许多实时性质,并且能够自动给出诊断信息．