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Showing papers on "Pushdown automaton published in 2001"


Book ChapterDOI
18 Jul 2001
TL;DR: An algorithm to generate Buchi automata from LTL formulae is presented and compared with Spin: the experiments show that the algorithm is much more efficient than Spin.
Abstract: We present an algorithm to generate Buchi automata from LTL formulae. This algorithm generates a very weak alternating co-Buchi automaton and then transforms it into a Buchi automaton, using a generalized Buchi automaton as an intermediate step. Each automaton is simplified on-the-fly in order to save memory and time. As usual we simplify the LTL formula before any treatment. We implemented this algorithm and compared it with Spin: the experiments show that our algorithm is much more efficient than Spin. The criteria of comparison are the size of the resulting automaton, the time of the computation and the memory used. Our implementation is available on the web at the following address: http://verif.liafa.jussieu.fr/ltl2ba

725 citations


Book ChapterDOI
01 Jan 2001
TL;DR: This chapter presents a hierarchy of infinite-state systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonly-studied classes of systems such as context-free and pushdown automata, and Petri net processes.
Abstract: In this chapter, we present a hierarchy of infinite-state systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonly-studied classes of systems such as context-free and pushdown automata, and Petri net processes. We then examine the equivalence and regularity checking problems for these classes, with special emphasis on bisimulation equivalence, stressing the structural techniques which have been devised for solving these problems. Finally, we explore the model checking problem over these classes with respect to various linear- and branching-time temporal logics.

240 citations


Journal ArticleDOI
TL;DR: In this article, an EXPTIME procedure for finding a winner in a pushdown game is presented, which is then used to solve the model-checking problem for the pushdown processes and the propositional?-calculus.
Abstract: 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 ?-calculus. The problem is shown to be DEXPTIME-complete.

211 citations


Journal ArticleDOI
29 Oct 2001
TL;DR: This paper considers LTL with regular valuations: the set of configurations satisfying an atomic proposition can be an arbitrary regular language and claims that the model-checking algorithms provide a general, unifying and efficient framework for solving them.
Abstract: 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.

174 citations


Journal ArticleDOI
TL;DR: In this article, an EXPTIME procedure for finding a winner in a pushdown game is presented, which is then used to solve the model-checking problem for the pushdown processes and the propositional μ-calculus.
Abstract: 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.

172 citations


Book ChapterDOI
18 Jul 2001
TL;DR: Since a timed automaton can be treated as a PTA without the pushdown stack, it can be shown that the binary reachability of a timedAutomaton is definable in the additive theory of reals and integers.
Abstract: We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a control state, dense clock values and a stack word. By using the pattern technique, we give a decidable characterization of the binary reachability (i.e., the set of all pairs of configurations such that one can reach the other) of a PTA. Since a timed automaton can be treated as a PTA without the pushdown stack, we can show that the binary reachability of a timed automaton is definable in the additive theory of reals and integers. The results can be used to verify a class of properties containing linear relations over both dense variables and unbounded discrete variables. The properties previously could not be verified using the classic region technique nor expressed by timed temporal logics for timed automata and CTL* for pushdown systems.

38 citations


Journal ArticleDOI
TL;DR: An O(|E|2) space and time algorithm to compute the equation automaton is presented, based on the notion of canonical derivative which makes it possible to efficiently handle sets of word derivatives.
Abstract: Two classical non-deterministic automata recognize the language denoted by a regular expression: the position automaton which deduces from the position sets defined by Glushkov and McNaughton–Yamada, and the equation automaton which can be computed via Mirkin's prebases or Antimirov's partial derivatives. Let |E| be the size of the expression and ‖E‖ be its alphabetic width, i.e. the number of symbol occurrences. The number of states in the equation automaton is less than or equal to the number of states in the position automaton, which is equal to ‖E‖+1. On the other hand, the worst-case time complexity of Antimirov algorithm is O(‖E‖3· |E|2), while it is only O(‖E‖·|E|) for the most efficient implementations yielding the position automaton (Bruggemann–Klein, Chang and Paige, Champarnaud et al.). We present an O(|E|2) space and time algorithm to compute the equation automaton. It is based on the notion of canonical derivative which makes it possible to efficiently handle sets of word derivatives. By the way, canonical derivatives also lead to a new O(|E|2) space and time algorithm to construct the position automaton.

34 citations


Journal ArticleDOI
TL;DR: This work uses process rewrite systems to describe infinite-state systems and defines a hierarchy of subclasses of PRS that includes Petri nets, pushdown processes, basic parallel processes (BPP), context-free processes and PA-Processes, and establishes the exact limits of the decidability of model checking with EF in this hierarchy.

30 citations


Book ChapterDOI
20 Aug 2001
TL;DR: A general reduction from labelled transition systems to unlabelled ones is suggested, preserving bisimilarity and satisfiability of µ-calculus formulas.
Abstract: In this paper we discuss the role of labels in transition systems with regard to bisimilarity and model checking problems. We suggest a general reduction from labelled transition systems to unlabelled ones, preserving bisimilarity and satisfiability of μ-calculus formulas. We apply the reduction to the class of transition systems generated by Petri nets and pushdown automata, and obtain several decidability/complexity corollaries for unlabelled systems. Probably the most interesting result is undecidability of strong bisimilarity for unlabelled Petri nets.

27 citations


Journal Article
TL;DR: It is proved that this regulation has no effect on the power of pushdown automata if the control languages are regular, however, the push down automata regulated by linear control languages characterize the family of recursively enumerable languages.
Abstract: The present paper suggests a new investigation area of the formal language theory—regulated automata Specifically, it investigates pushdown automata that regulate the use of their rules by control languages It proves that this regulation has no effect on the power of pushdown automata if the control languages are regular However, the pushdown automata regulated by linear control languages characterize the family of recursively enumerable languages All these results are established in terms of (A) acceptance by final state, (B) acceptance by empty pushdown, and (C) acceptance by final state and empty pushdown In its conclusion, this paper formulates several open problems

24 citations



Book ChapterDOI
27 Aug 2001
TL;DR: It is shown that for all n and α such that 1 ≤ n ≤ α ≤ 2n there is a minimal n-state nondeterministic finite automaton whose equivalent minimal deterministic automaton has exactly α states.
Abstract: We show that for all n and α such that 1 ≤ n ≤ α ≤ 2n there is a minimal n-state nondeterministic finite automaton whose equivalent minimal deterministic automaton has exactly α states.

Journal ArticleDOI
TL;DR: This paper provides a proof of an earlier conjecture by Moller: that multiset automata form a proper subset of Petri nets, which contrasts with the result of Caucal for the analogous question in the sequential case where the hierarchy collapses.

Book ChapterDOI
02 Apr 2001
TL;DR: For full Petri nets Jancar proved that bisimulation equivalence is undecidable, and decidability of bisimilarity was also shown for Basic Parallel processes, a restricted subset of Petrinets.
Abstract: In the past decade there has been a variety of results showing decidability of bisimulation equivalence between infinite state systems. The initial result, due to Baeten, Bergstra and Klop [1], proved decidability for normed BPA processes, described using irredundant context-free grammars. This was extended to all BPA processes and then to pushdown automata [5,16,14]. Decidability of bisimilarity was also shown for Basic Parallel (BP) processes, a restricted subset of Petri nets, [4]. For full Petri nets Jancar proved that bisimulation equivalence is undecidable [11].

Journal ArticleDOI
TL;DR: It is shown that for each positive integer n, there is a nondeterministic finite automaton An over a two-letter alphabet such that An has n states, whereas the smallest equivalent nondegenerate sweeping automaton has 2n states.

Book ChapterDOI
01 Jul 2001
TL;DR: An O(s2) space and time algorithm to compute the equation automaton based on the notion of canonical derivative which is related both to word and partial derivatives is presented.
Abstract: Let E be a regular expression the size of which is s. Mirkin's prebases and Antimirov's partial derivatives lead to the construction of the same automaton, called the equation automaton of E. The number of states in this automaton is less than or equal to the number of states in the position automaton. On the other hand, it can be computed by Antimirov's algorithm with an O(s5) time complexity, whereas there exist O(s2) implementations for the position automaton. We present an O(s2) space and time algorithm to compute the equation automaton. It is based on the notion of canonical derivative which is related both to word and partial derivatives. This work is tightly connected to pattern matching area since the aim is, given a regular expression, to produce an as small as possible recognizer with the best space and time complexity.

Journal Article
TL;DR: An O(s 2 ) space and time algorithm to compute the equation automaton of E, based on the notion of canonical derivative which is related both to word and partial derivatives is presented.
Abstract: Let E be a regular expression the size of which is s. Mirkin's prebases and Antimirov's partial derivatives lead to the construction of the same automaton, called the equation automaton of E. The number of states in this automaton is less than or equal to the number of states in the position automaton. On the other hand, it can be computed by Antimirov's algorithm with an O(s 5 ) time complexity, whereas there exist O(s 2 ) implementations for the position automaton. We present an O(s 2 ) space and time algorithm to compute the equation automaton. It is based on the notion of canonical derivative which is related both to word and partial derivatives. This work is tightly connected to pattern matching area since the aim is, given a regular expression, to produce an as small as possible recognizer with the best space and time complexity.

Journal Article
TL;DR: In this paper, the necessary and sufficient conditions for an automaton to be locally threshold testable are found, and the first polynomial time algorithm to verify local threshold testability of the automaton based on this characterization is introduced.
Abstract: A locally threshold testable language L is a language with the property that for some nonnegative integers k and l, whether or not a word u is in the language L depends on (1) the prefix and suffix of the word u of length k-1 and (2) the set of intermediate substrings of length k of the word u where the sets of substrings occurring at least j times are the same, for j < l. For given k and I the language is called l-threshold k-testable. A finite deterministic automaton is called l-threshold k-testable if the automaton accepts a l-threshold k-testable language. In this paper, the necessary and sufficient conditions for an automaton to be locally threshold testable are found. We introduce the first polynomial time algorithm to verify local threshold testability of the automaton based on this characterization. New version of polynomial time algorithm to verify the local testability will be presented too.


Book ChapterDOI
16 Jul 2001
TL;DR: The power of randomization for pushdown automata is investigated by investigating the power of decreasing error probabilities, and it is shown that deterministic push down automata are weaker than Las Vegas pushdown Automata, which in turn are stronger than one-sided-error pushdownAutomata.
Abstract: Although randomization is now a standard tool for the design of efficient algorithms or for building simpler systems, we are far from fully understanding the power of randomized computing. Hence it is advisable to study randomization for restricted models of computation.We followthis approach by investigating the power of randomization for pushdown automata.Our main results are as follows. First we show that deterministic pushdown automata are weaker than Las Vegas pushdown automata, which in turn are weaker than one-sided-error pushdown automata. Finally one-sided-error pushdown automata are weaker than (nondeterministic) pushdown automata.In contrast to many other fundamental models of computing there are no known methods of decreasing error probabilities.We show that such methods do not exist by constructing languages which are recognizable by one-sided-error pushdown automata with error probability 1/2, but not by one-sided-error pushdown automata with error probability p < 1/2. On the other hand we construct languages which are not deterministic context-free (resp. not context-free) but are recognizable with arbitrarily small error by one-sided-error (resp. bounded-error) pushdown automata.

Book ChapterDOI
28 Aug 2001
TL;DR: This paper aims at synthesizing an executable specification for a real- time system by integrating real-time scenarios into a timed automaton which simulates the behaviors specified by the scenarios.
Abstract: In this paper, we aim at synthesizing an executable specification for a real-time system by integrating real-time scenarios into a timed automaton. A scenario represents a partial description of a system behavior. A formal semantics is given for the model of a scenario and is used to compile a scenario into a timed automaton. The compilation algorithm is generalized to integrate several scenarios into a single timed automaton which simulates the behaviors specified by the scenarios. The results of the compilation algorithm are independent of the order in which the scenarios are added.

Journal ArticleDOI
TL;DR: A general reduction from labelled transition systems to unlabelled ones is suggested, preserving bisimilarity and satisfiability of mu-calculus formulas.
Abstract: In this paper we discuss the role of labels in transition systems with regard to bisimilarity and model checking problems. We suggest a general reduction from labelled transition systems to unlabelled ones, preserving bisimilarity and satisfiability of mu-calculus formulas. We apply the reduction to the class of transition systems generated by Petri nets and pushdown automata, and obtain several decidability/complexity corollaries for unlabelled systems. Probably the most interesting result is undecidability of strong bisimilarity for unlabelled Petri nets.

01 Jan 2001
TL;DR: In this paper, the authors study the descriptional complexity of cellular automata, and show that between one of the simplest cellular models, the real-time one-way CA (real-time-OCA), and "classical" models like deterministic finite automata or pushdown automata there will be savings concerning the size of description not bounded by any recursive function, so-called nonrecursive trade-offs.
Abstract: We study the descriptional complexity of cellular automata (CA) which are a parallel model of computation. We show that between one of the simplest cellular models, the realtime one-way CA (realtime-OCA), and "classical" models like deterministic finite automata or pushdown automata, there will be savings concerning the size of description not bounded by any recursive function, so-called nonrecursive trade-offs. Furthermore, nonrecursive trade-offs are shown to exist between certain restricted classes of cellular automata. The set of valid computations of a Turing machine can be recognized by a realtime-OCA. This implies that many decidability questions are not even semidecidable for cellular automata. There is no pumping lemma and no minimization algorithm for cellular automata. Finally, we prove that the language class accepted by realtime-OCA is incomparable to many known and well-investigated language classes.

Proceedings ArticleDOI
17 Apr 2001
TL;DR: Presents a methodology for using a 'parallel automaton' to set up the requirements, to specify and to execute small computer-based systems (CBSs) and gives an architecture of a virtual machine that is built to execute such a parallel automaton on a network.
Abstract: Presents a methodology for using a 'parallel automaton' to set up the requirements, to specify and to execute small computer-based systems (CBSs). A parallel automaton is an extended form of the Mealy machine. It handles a finite set of events (variable conditions or clock conditions) which can occur in parallel, and performs a finite set of actions which can be carried out in parallel. In the parallel automaton, there is no concept of a "global state" as in the Mealy machine. Instead, to each action and to each event is associated a "private state" representing their occurrence in the application. Nevertheless, the number of event/action private states is also finite. This single notation (a parallel automaton with private states) can be used to describe requirements and specifications in the same way. Moreover, these two descriptions can be connected. The aims of the application can be described using a parallel automaton as a black box with initial inputs and final outputs. This parallel automaton can then be refined and enhanced with intermediate conditions and actions to obtain detailed requirements. By successive refinements and enhancements, a sufficiently detailed executable specification can be derived. We present this methodology through a simple CBS example for requirements and specifications using the parallel automaton notation. We then give an architecture of a virtual machine that we have built to execute such a parallel automaton on a network.

Journal ArticleDOI
TL;DR: This result acts as a complete relationship between languages of type r − generated by SE-systems of type (reg,reg,f) and stack languages of pushdown automata.


Book ChapterDOI
13 Dec 2001
TL;DR: Senizergues as mentioned in this paper showed that two pushdown automata are equivalent if, and only if, there is a finite proof of this fact, where the equations within the proof system have associated weights.
Abstract: The DPDA equivalence problem was posed in 1966 [4]: is there an effective procedure for deciding whether two configurations of a deterministic pushdown automaton (a DPDA) accept the same language? The problem is whether language equivalence is decidable for deterministic context-free languages. Despite intensive work throughout the late 1960s and 1970s, the problem remained unsolved until 1997 when Senizergues announced a positive solution [11]. It seems that the notation of pushdown configurations, although simple, is not rich enough to sustain a proof. Deeper algebraic structure needs to be exposed. The full proof by Senizergues, in journal form, appeared earlier this year [12]. It exposes structure within a DPDA by representing configurations as boolean rational series, and he develops an algebraic theory of their linear combinations. Equivalence between configurations is captured within a deduction system. The equations within the proof system have associated weights. Higher level strategies (transformations) are defined which guide proof. A novel feature is that these strategies depend upon differences between weights of their associated equations. Decidability is achieved by showing that two configurations are equivalent if, and only if, there is a finite proof of this fact.

Posted Content
TL;DR: In this paper, the notion of quantum pushdown automata (QPA) was introduced in a non-equivalent way by using the definition of quantum finite automata of Kondacs and Watrous.
Abstract: Quantum finite automata, as well as quantum pushdown automata (QPA) were first introduced by C. Moore and J. P. Crutchfield. In this paper we introduce the notion of QPA in a non-equivalent way, including unitarity criteria, by using the definition of quantum finite automata of Kondacs and Watrous. It is established that the unitarity criteria of QPA are not equivalent to the corresponding unitarity criteria of quantum Turing machines. We show that QPA can recognize every regular language. Finally we present some simple languages recognized by QPA, not recognizable by deterministic pushdown automata.

Journal Article
TL;DR: This paper defines a particular type of timed push down automata and shows that the emptiness problem for this class is decidable, and presents a notion of homomorphism and parallel decomposition for these automata.
Abstract: In this paper we define a particular type of timed push down automata. We show that the emptiness problem for this class is decidable. We also present a notion of homomorphism and parallel decomposition for these automata. These notions are a generalisation of the homomorphism and decomposition via partitions for finite automata.

Journal ArticleDOI
TL;DR: This paper investigates infinite hierarchies on alternation-depth andAlternation-size of alternating pushdown automata (apda's) with sublogarithmic space and shows that there is an infinite hierarchy on alternated-size.