Efficient determinization of visibly and height-deterministic pushdown automata

New algorithms for the determinization of nondeterministic visibly and nondeterministic real-time height-deterministic pushdown automata are presented. The algorithms improve the results of existing algorithms. They construct only accessible states and necessary pushdown symbols of the resulting deterministic pushdown automata.     

LINEAR ITERATED PUSHDOWNS

This paper discusses variants of nondeterministic one-way S -automata and context-free S -grammars where S is a storage type. The framework that these systems provide can be used to give alternative formulations of embedded pushdown automata and linear indexed grammars. The embedded pushdown automata is obtained by means of a linear version of a class of storage types called iterated pushdowns. Linear indexed grammar is obtained by using the pushdown storage type and restricting the way in which the grammar uses its storage.     

Pushdown Processes: Games and Model-Checking

A pushdown game is a two player perfect information infinite game on a transition graph of a pushdown automaton. A winning condition in such a game is defined in terms of states appearing infinitely often in the play. It is shown that if there is a winning strategy in a pushdown game then there is a winning strategy realized by a pushdown automaton. An EXPTIME procedure for finding a winner in a pushdown game is presented. The procedure is then used to solve the model-checking problem for the pushdown processes and the propositional μ-calculus. The problem is shown to be DEXPTIME-complete.     

Characterizations and extensions of pushdown translations

A device called a pushdown assembler has been recently introduced and has been shown capable of defining exactly the syntax directed translations (SDT's). The output operation of the pushdown assembler can be extended in a natural way to obtain a more powerful device called a type B pushdown assembler (or B-machine). A B-machine can define SDT's more simply and directly than the original pushdown assembler. B-machines can also define many interesting translations which are not SDT's. In this paper the B-machine is defined and compared with the original pushdown assembler. The properties of B-machine translations are investigated and it is shown that, as with SDT's, there exists a natural infinite hierarchy of B-machine translations.     

Model checking LTL with regular valuations for pushdown systems

Recent works have proposed pushdown systems as a tool for analyzing programs with (recursive) procedures, and the model-checking problem for LTL has received special attention. However, all these works impose a strong restriction on the possible valuations of atomic propositions: whether a configuration of the pushdown system satisfies an atomic proposition or not can only depend on the current control state of the pushdown automaton and on its topmost stack symbol. In this paper we consider LTL with regular valuations: the set of configurations satisfying an atomic proposition can be an arbitrary regular language. The model-checking problem is solved via two different techniques, with an eye on efficiency. The resulting algorithms are polynomial in certain measures of the problem which are usually small, but can be exponential in the size of the problem instance. However, we show that this exponential blowup is inevitable. The extension to regular valuations allows to model problems in different areas; for instance, we show an application to the analysis of systems with checkpoints. We claim that our model-checking algorithms provide a general, unifying and efficient framework for solving them.     

On LR(k) grammars and languages

Many different definitions for LR(k) grammars exist in the literature. One of these definitions is chosen and many important implications are drawn from it. In particular, the LR(k) characterization theorem provides valuable information about chains of derivations. The LR(0) languages are then characterized by acceptance by deterministic pushdown automata with a special termination condition, by a condition on the strings in the language, and set theoretically. Important closure properties of the LR(0) languages and a related class of languages are then examined. These are used to examine some decidability questions relating to the class of LR languages. One of these questions is shown to be equivalent to the equality problem for deterministic pushdown automata.A survey of other LR(k) definitions is given and the exact differences are characterized. On the basis of this analysis, justification for the choice of definition used here is provided.     

Spinal-Formed Context-Free Tree Grammars

In this paper we introduce a restricted model of context-free tree grammars called spine grammars, and study their formal properties including considerably simple normal forms. Recent research on natural languages has suggested that formalisms for natural languages need to generate a slightly larger class of languages than context-free grammars, and for that reason tree adjoining grammars have been widely studied relating them to natural languages. It is shown that the class of string languages generated by spine grammars coincides with that of tree adjoining grammars. We also introduce acceptors called linear pushdown tree automata, and show that linear pushdown tree automata accept exactly the class of tree languages generated by spine grammars. Linear pushdown tree automata are obtained from pushdown tree automata with a restriction on duplicability for the pushdown stacks. Received May 29, 1998, and in revised form April 27, 1999, and in final form May 10, 1999.     

Model checking dynamic pushdown networks

A dynamic pushdown network (DPN) is a set of pushdown systems (PDSs) where each process can dynamically create new instances of PDSs. DPNs are a natural model of multi-threaded programs with (possibly recursive) procedure calls and thread creation. Thus, it is important to have model checking algorithms for DPNs. We consider in this work model checking DPNs against single-indexed LTL and CTL properties of the form \({\bigwedge f_i}\) such that f _i is a LTL/CTL formula over the PDS i. We consider the model checking problems w.r.t. simple valuations (i.e., whether a configuration satisfies an atomic proposition depends only on its control location) and w.r.t. regular valuations (i.e., the set of the configurations satisfying an atomic proposition is a regular set of configurations). We show that these model checking problems are decidable. We propose automata-based approaches for computing the set of configurations of a DPN that satisfy the corresponding single-indexed LTL/CTL formula.     

A note on deciding controllability in pushdown systems

Consider an event alphabet /spl Sigma/. The supervisory control theory of Ramadge and Wonham asks the question, given a plant model G, with language K L/sub M/(G)/spl sube//spl Sigma//sup */ and another language K/spl sube/ L/sub M/(G), is there a supervisor /spl psi/ such that L/sub M/(/spl psi//G)=K. Ramadge and Wonham showed that a necessary condition for this to be true is the so-called controllability of K with respect to L/sub M/(G). They showed that when G is a finite state automaton and K is a regular language (also generated by a finite state automaton), then the controllability property was decidable for K. The class of languages generated by pushdown automata properly includes the regular languages. They are accepted by finite state machines coupled with pushdown stack memory. This makes them interesting candidates as supervisory languages, since the supervisor will have nonfinite memory. In this note, we show the following: i) If S is a specification given by a deterministic pushdown automaton and L is generated by a finite state machine, then there is an algorithm to decide whether K=S/spl cap/L is controllable with respect to L. ii) It is undecidable for an arbitrary specification S generated by a nondeterministic pushdown automaton and plant language L generated by a finite state machine whether K=S/spl cap/L is controllable with respect to L.     

A note on non-singular deterministic pushdown automata

The non-singular deterministic pushdown automata were first defined by Valiant as an example of a class of machines with a decidable equivalence problem [3]. No algorithm currently exist for deciding whether or not a deterministic pushdown automation is non-singular, so the applicability of Valiant's equivalence decision procedure cannot be readily (if ever) determined. In this paper, it is shown that the equivalence problem for non-singular automata is reducible to the problem of deciding whether or not a deterministic pushdown automaton is non-singular.     

Measuring nondeterminism in pushdown automata

The amount of nondeterminism that a pushdown automaton requires to recognize an input string can be measured by the minimum number of guesses that it must make to accept the string, where guesses are measured in bits of information. When this quantity is unbounded, the rate at which it grows as the length of the string increases serves as a measure of the pushdown automaton's “rate of consumption” of nondeterminism. We show that this measure is similar to other complexity measures in that it gives rise to an infinite hierarchy of complexity classes of context-free languages differing in the amount of the resource (in this case, nondeterminism) that they require. In addition, we show that there are context-free languages that can only be recognized by a pushdown automaton whose nondeterminism grows linearly, resolving an open problem in the literature. In particular, the set of palindromes is such a language.     

量化上下文无关语言的代数性质

通过引入量化下推自动机与量化上下文无关文法的定义,研究了以两种不同方式接受语言的量化下推自动机等价性问题,证明了在可交换的双幺赋值幺半群上,量化下推自动机接受的语言与量化上下文无关文法生成的语言相同。     

On regular tree languages and deterministic pushdown automata

The theory of formal string languages and of formal tree languages are both important parts of the theory of formal languages. Regular tree languages are recognized by finite tree automata. Trees in their postfix notation can be seen as strings. This paper presents a simple transformation from any given (bottom-up) finite tree automaton recognizing a regular tree language to a deterministic pushdown automaton accepting the same tree language in postfix notation. The resulting deterministic pushdown automaton can be implemented easily by an existing parser generator because it is constructed for an LR(0) grammar, and its size directly corresponds to the size of the deterministic finite tree automaton. The class of regular tree languages in postfix notation is a proper subclass of deterministic context-free string languages. Moreover, the class of tree languages which are in their postfix notation deterministic context-free string languages is a proper superclass of the class of regular tree languages.     

Reachability of Patterned Conditional Pushdown Systems

Conditional pushdown systems (CPDSs) extend pushdown systems by associating each transition rule with a regular language over the stack alphabet. The goal is to model program verification problems that need to examine the runtime call stack of programs. Examples include security property checking of programs with stack inspection, compatibility checking of HTML5 parser specifications, etc. Esparza et al. proved that the reachability problem of CPDSs is EXPTIME-complete, which prevents the existence of an algorithm tractable for all instances in general. Driven by the practical applications of CPDSs, we study the reachability of patterned CPDS (pCPDS) that is a practically important subclass of CPDS, in which each transition rule carries a regular expression obeying certain patterns. First, we present new saturation algorithms for solving state and configuration reachability of pCPDSs. The algorithms exhibit the exponential-time complexity in the size of atomic patterns in the worst case. Next, we show that the reachability of pCPDSs carrying simple patterns is solvable in fixed-parameter polynomial time and space. This answers the question on whether there exist tractable reachability analysis algorithms of CPDSs tailored for those practical instances that admit efficient solutions such as stack inspection without exception handling. We have evaluated the proposed approach, and our experiments show that the pattern-driven algorithm steadily scales on pCPDSs with simple patterns.

     

Pushdown tree automata

We define topdown pushdown tree automata (PDTA's) which extend the usual string pushdown automata by allowing trees instead of strings in both the input and the stack. We prove that PDTA's recognize the class of context-free tree languages. (Quasi)realtime and deterministic PDTA's accept the classes of Greibach and deterministic tree languages, respectively. Finally, PDTA's are shown to be equivalent to restricted PDTA's, whose stack is linear: this both yields a more operational way of recognizing context-free tree languages and connects them with the class of indexed languages.     

基于DNA计算的分子下推自动机(英文)

DNA分子计算的工作原理是对生物系统进行编码,以生物化学反应为基础,利用生物技术实现生物系统的状态转移来推进计算过程．2001年以色列的Yaakov Benenson等人在基于DNA计算的发卡模型实现了具有状态转移功能的分子有限状态自动机,国内则有利用DNA计算的方法构造可编程分子下推存储器的相关研究．该存储器基于分子自动机的原理,能按一定逻辑进行自组装,是一种纳米尺度的生物存储机构．文中首先通过在分子有限自动机上扩展一个分子下推存储器从而获得了一种简单的分子下推自动机,并基于该下推自动机提出了一类语言的分子自动机解法．接着提出了两种改进的分子下推自动机的模型,通过增加模型复杂度,分别解决了基本型分子下推自动机存在输人字符串限制和输入分子形式不统一的问题．计算理论表明,该种下推自动机的计算能力超过了已有的有限自动机．     

Conjunctive grammars and alternating pushdown automata

In this paper we introduce a variant of alternating pushdown automata, synchronized alternating pushdown automata, which accept the same class of languages as those generated by conjunctive grammars.     

Simple chain grammars and languages

A subclass of the LR(0)-grammars, the class of simple chain grammars is introduced. Although there exist simple chain grammars which are not LL(k) for any k>0, this new class of grammars is very closely related to the LL(1) and simple LL(1) grammars. In fact it can be shown that every simple chain grammar has an equivalent simple LL(1) grammar.Cover properties for simple chain grammars are investigated and a deterministic pushdown transducer which acts as a right parser for simple chain grammars is presented.     

Model checking probabilistic systems against pushdown specifications

Model checking is a fully automatic verification technique traditionally used to verify finite-state systems against regular specifications. Although regular specifications have been proven to be feasible in practice, many desirable specifications are non-regular. For instance, requirements which involve counting cannot be formalized by regular specifications but using pushdown specifications, i.e., context-free properties represented by pushdown automata. Research on model-checking techniques for pushdown specifications is, however, rare and limited to the verification of non-probabilistic systems.In this paper, we address the probabilistic model-checking problem for systems modeled by discrete-time Markov chains and specifications that are provided by deterministic pushdown automata over infinite words. We first consider finite-state Markov chains and show that the quantitative and qualitative model-checking problem is solvable via a product construction and techniques that are known for the verification of probabilistic pushdown automata. Then, we consider recursive systems modeled by probabilistic pushdown automata with an infinite-state Markov chain semantics. We first show that imposing appropriate compatibility (visibility) restrictions on the synchronizations between the pushdown automaton for the system and the specification, decidability of the probabilistic model-checking problem can be established. Finally we prove that slightly departing from this compatibility assumption leads to the undecidability of the probabilistic model-checking problem, even for qualitative properties specified by deterministic context-free specifications.