Folk theorems on the determinization and minimization of timed automata

Timed automata are known not to be complementable or determinizable. Natural questions are, then, could we check whether a given TA enjoys these properties? These problems are not algorithmically solvable. Minimizing the “resources” of a TA (number of clocks or size of constants) are also unsolvable problems. In this paper we provide simple undecidability proofs using a “constructive” version of the problems where we require not just a yes/no answer, but also a “witness”. Proofs are then simple reductions from the universality problem. Recent work of Finkel shows that the corresponding decision problems are also undecidable [O. Finkel, On decision problems for timed automata, Bulletin of the European Association for Theoretical Computer Science 87 (2005) 185-190].     

采用树自动机推理技术的信息抽取方法

提出了一种利用改进的k-contextual树自动机推理算法的信息抽取技术。其核心思想是将结构化（半结构化）文档转换成树,然后利用一种改进的k-contextual树（KLH树）来构造出能够接受样本的无秩树自动机,依据该自动机接收和拒绝状态来确定是否抽取网页信息。该方法充分利用了网页文档的树状结构,依托树自动机将传统的以单一结构途径的信息抽取方法与文法推理原则相结合,得到信息抽取规则。实验证明,该方法与同类抽取方法相比,样本学习时间以及抽取所需时间上均有所缩短。     

A multidimensional approach to syntactic pattern recognition

This paper describes a syntactic method for representing the primitive parts of a pattern as nodes of a type of directed graph. A linear representation of the digraph can then be presented to a regular unordered tree automaton for classification. Regular unordered tree automata can be simulated by deterministic pushdown automata, so this procedure can be implemented easily. Regular u-tree automata and the corresponding generative systems, regular u-tree grammars are formally defined. Several results are shown which are applicable to all syntactic pattern recognition schemes involving the use of primitives.     

Abstract Regular Tree Model Checking

Regular (tree) model checking (RMC) is a promising generic method for formal verification of infinite-state systems. It encodes configurations of systems as words or trees over a suitable alphabet, possibly infinite sets of configurations as finite word or tree automata, and operations of the systems being examined as finite word or tree transducers. The reachability set is then computed by a repeated application of the transducers on the automata representing the currently known set of reachable configurations. In order to facilitate termination of RMC, various acceleration schemas have been proposed. One of them is a combination of RMC with the abstract-check-refine paradigm yielding the so-called abstract regular model checking (ARMC). ARMC has originally been proposed for word automata and transducers only and thus for dealing with systems with linear (or easily linearisable) structure. In this paper, we propose a generalisation of ARMC to the case of dealing with trees which arise naturally in a lot of modelling and verification contexts. In particular, we first propose abstractions of tree automata based on collapsing their states having an equal language of trees up to some bounded height. Then, we propose an abstraction based on collapsing states having a non-empty intersection (and thus “satisfying”) the same bottom-up tree “predicate” languages. Finally, we show on several examples that the methods we propose give us very encouraging verification results.     

运用时间分类树的确定单时钟时间自动机学习

时间自动机的模型学习算法旨在通过提供输入和观察输出构建软硬件系统的形式化模型.确定性单时钟时间自动机的学习是其中的一个重要研究方向, 但是该算法具有一定的局限性, 在状态较多时学习速度较慢, 很难应用到复杂的系统中.由此, 我们提出了一种改进的学习算法, 使用逻辑时间分类树代替逻辑时间观察表作为学习算法的内部数据结构, 有效地减少了成员查询次数, 降低了算法的空间复杂度, 并能够高效率地构建假设自动机.最后我们进行了相关实验, 实验结果表明, 本文提出的改进算法减少了60%左右的成员查询和5%左右的等价查询.同时在该实验中, 改进算法的学习速度最高可提高45倍以上.     

模糊树自动机语言的封闭性

给出了[Σ-]代数、[Σ-]树、模糊[Σ-]树自动机、模糊[Σ-]树自动机行为的定义。引入了模糊树自动机语言的并、交、连接和Kleene闭包运算,证明了在这些运算下模糊树自动机语言的封闭性。     

Closure properties and decision problems of dag automata

Tree automata are widely used in various contexts. They are closed under boolean operations and their emptiness problem is decidable in polynomial time. Dag automata are natural extensions of tree automata, operating on dags instead of on trees; they can also be used for solving problems. Our purpose in this paper is to show that algebraically they behave differently: the class of dag automata is not closed under complementation, dag automata are not determinizable, their membership problem is NP-complete, the universality problem is undecidable, and the emptiness problem is NP-complete even for deterministic labeled dag automata.     

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.     

格值树自动机与格值上下文无关树文法的等价性

本文将模糊树自动机和模糊上下文无关树文法的概念推广到格半群上。证明了在接受语言和生成语言的意义下,树自动机和上下文无关树文法是等价的。同时给出了构造正规形式的等价文法的方法。     

Infinitary tree languages recognized by ω-automata

We define top-down infinite tree automata (ω-automata) which is an extension of Rabin's automata to infinite Σ-tress. We prove that each ω-automaton can be completed to an equivalent one and that non-deterministic ω-automata have more power than deterministic ω-automata. We study the difference between ω-languages and deterministic ω-languages by using AFL-like operations.     

Inference of tree automata from sample set of trees

A method for inferring of tree automata from sample set of trees is presented. The procedure, which is based on the concept ofk-follower of a tree with respect to the sample tree set, produces a tree automaton capable of accepting all the sample trees as well as other trees similar in structure. The behavior of the inferred tree automaton for varying values of parameterk is also discussed.This work was supported in part by a Scientific Research Grant-In-Aid (Grant No. 57460129) from the Ministry of Education, Science and Culture, Japan.     

一种基于DTD的XPath逻辑优化方法

Xpath成为XML数据查询的基本机制.Xpath中表达节点之间的祖孙关系的‘//'和任意匹配字符的‘*'等非确定操作符,增强了Xpath表达方式的灵活性,但同时引入了Xpath处理的复杂性.如何利用DTD减少Xpath中的不确定操作符,从而提高Xpath的执行效率成为一个基本的研究问题.传统方法主要侧重于特定受限Xpath的确定化重写.利用树自动机在一个框架中表达Xpath和DTD,提出了一种新的Xpath树自动机和DTD树自动机的乘积运算,并证明了乘积的结果就是基于DTD的Xpath优化形式,在多项式时间内基于代价获取了Xpath的优化结果.实验数据表明,基于提出的Xpath的逻辑优化方法,能够有效地提高Xpath执行器的执行效率.     

Rigid tree automata and applications

We introduce the class of rigid tree automata (RTA), an extension of standard bottom-up automata on ranked trees with distinguished states called rigid. Rigid states define a restriction on the computation of RTA on trees: RTA can test for equality in subtrees reaching the same rigid state. RTA are able to perform local and global tests of equality between subtrees, non-linear tree pattern matching, and some inequality and disequality tests as well. Properties like determinism, pumping lemma, Boolean closure, and several decision problems are studied in detail. In particular, the emptiness problem is shown decidable in linear time for RTA whereas membership of a given tree to the language of a given RTA is NP-complete. Our main result is the decidability of whether a given tree belongs to the rewrite closure of an RTA language under a restricted family of term rewriting systems, whereas this closure is not an RTA language. This result, one of the first on rewrite closure of languages of tree automata with constraints, is enabling the extension of model checking procedures based on finite tree automata techniques, in particular for the verification of communicating processes with several local non-rewritable memories, like security protocols. Finally, a comparison of RTA with several classes of tree automata with local and global equality tests, with dag automata and Horn clause formalisms is also provided.     

基于树自动机的XPath在XML数据流上的高效执行

如何在XML数据流上高效地执行大量的XPath查询成为数据流应用中一个迫切需要解决的关键问题.目前提出的算法或者不能完全支持XPath的常规特性,或者在算法的执行效率和空间代价上不能满足数据流应用的要求.提出了基于树自动机的XEBT机来解决这个问题.与传统方法相比,XEBT机具备如下特征:首先,XEBT机基于表达能力丰富的树自动机,无须附加中间状态,或保存中间结果,就能处理支持{[]}操作符的XPath;其次,XEBT机支持多种优化策略,包括基于DTD的XPath查询自动机的构造;在空间代价有限增加的情况下采用局部确定化减少并发执行的状态;采用自上而下和自下而上相结合的查询处理策略.实验结果表明,提出的方法能够支持复杂的XPath查询,在执行效率和空间代价方面优于传统算法.     

The complexity of tree automata and XPath on grammar-compressed trees

The complexity of various membership problems for tree automata on compressed trees is analyzed. Two compressed representations are considered: dags, which allow to share identical subtrees in a tree, and straight-line context-free tree grammars, which moreover allow to share identical intermediate parts in a tree. Several completeness results for the classes NL, P, and PSPACE are obtained. Finally, the complexity of the evaluation problem for (structural) XPath queries on trees that are compressed via straight-line context-free tree grammars is investigated.     

基于树自动机的XML过滤技术

为了提高XML数据流的查询匹配效率,基于XML过滤技术研究提出了一种基于树自动机的XML过滤技术XTAFilter.该技术利用hash表来存储谓词,并对多个查询表达式XPath通过共享路径构建树自动机,减少了匹配的时间,提高了查询匹配的效率,同时降低系统运行时的活动状态.搭建仿真平台对技术进行验证,仿真实验结果表明,XTAFilter 技术能有效地提高XML数据流的匹配效率,提高了系统的实用性.     

From Syntactic Theories to Interpreters: Automating the Proof of Unique Decomposition

Developing syntactic theories for reasoning about programming languages usually involves proving a unique-decomposition lemma. The proof of such a lemma is tedious, error-prone, and is usually attempted many times during the design of a theory. We therefore investigate the automation of such proofs.We map the unique-decomposition lemma to the problems of checking equivalence and ambiguity of syntactic definitions. Because checking these properties of context-free grammars is undecidable, we work with regular tree grammars and use algorithms on finite tree automata to perform the checking. To make up for the insufficient expressiveness of regular tree grammars, we extend the basic framework with built-in types and constants, contexts, and polymorphic types.Our implementation extends an earlier system by Xiao et al. [16] that translates semantic specifications expressed as syntactic theories to interpreters. We have successfully used the combined system to generate interpreters and verify the unique-decomposition lemma for a number of examples.     

Compiling CSPs into Tree-Driven Automata for Interactive Solving

Constraint programming techniques are widely used to model and solve decision problems and many algorithms have been developed to solve automatically and efficiently families of CSPs; nevertheless, they do not help solve interactive decision support problems, like product configuration. In such problems, the user chooses the values of the variables, and the role of the system is not to solve the CSP, but to help the user in this task. Dynamic global consistency maintaining is one of the most useful functionalities that should be offered by such a CSP platform. Unfortunately, this task is intractable in the worst case. Since interactivity requires short response times, intractability must be circumvented some way. To this end, compilation methods have been proposed that transform the original problem into a data structure allowing a short response time. In this paper, we extend the work of Amilhastre et al. [1] and Vempaty [15] by the use of a new structure, tree-driven automata, that takes advantage of the structural characteristics of configuration problems (decomposition of the components into independent subcomponents). Tree-driven automata can be far more compact than classical automata while keeping their good properties, especially a tractable complexity for the maintenance of global consistency.     

ACTAS : A System Design for Associative and Commutative Tree Automata Theory

ACTAS is an integrated system for manipulating associative and commutative tree automata (AC-tree automata for short), that has various functions such as for Boolean operations of AC-tree automata, computing rewrite descendants, and solving emptiness and membership problems. In order to deal with high-complexity problems in reasonable time, over- and under-approximation algorithms are also equipped. Such functionality enables us automated verification of safety property in infinite state models, that is helpful in the domain of, e.g. network security, in particular, for security problems of cryptographic protocols allowing an equational property. In runtime of model construction, a tool support for analysis of state space expansion is provided. The intermediate status of the computation is displayed in numerical data table, and also the line graphs are generated. Besides, a graphical user interface of the system provides us a user-friendly environment for handy use.     

Active XML文档安全重写判定算法

研究了AXML文档安全重写判定问题,即判定给定AXML文档通过触发其包含的服务调用生成的文档集合是否能够全部重写为符合目标模式的文档实例.基于树自动机理论,定义了用于抽象AXML文档的树自动机--ATA机(AXML treeautomata),ATA机等价于给定AXML文档通过触发其包含的服务调用所能生成的文档集合.基于ATA机,提出一个AXML文档安全重写判定算法,表明了该算法的正确性及有效性.