Topic
Pushdown automaton
About: Pushdown automaton is a research topic. Over the lifetime, 1868 publications have been published within this topic receiving 35399 citations.
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25 Jun 2012
TL;DR: It is shown that computations of several known models of systems can be encoded as multi-head pushdown automata, giving uniform and optimal underapproximation algorithms modulo bounded languages.
Abstract: A class of languages C is perfect if it is closed under Boolean operations and the emptiness problem is decidable. Perfect language classes are the basis for the automata-theoretic approach to model checking: a system is correct if the language generated by the system is disjoint from the language of bad traces. Regular languages are perfect, but because the disjointness problem for CFLs is undecidable, no class containing the CFLs can be perfect. In practice, verification problems for language classes that are not perfect are often under-approximated by checking if the property holds for all behaviors of the system belonging to a fixed subset. A general way to specify a subset of behaviors is by using bounded languages (languages of the form w1* ... wk* for fixed words w1,...,wk). A class of languages C is perfect modulo bounded languages if it is closed under Boolean operations relative to every bounded language, and if the emptiness problem is decidable relative to every bounded language. We consider finding perfect classes of languages modulo bounded languages. We show that the class of languages accepted by multi-head pushdown automata are perfect modulo bounded languages, and characterize the complexities of decision problems. We also show that bounded languages form a maximal class for which perfection is obtained. We show that computations of several known models of systems, such as recursive multi-threaded programs, recursive counter machines, and communicating finite-state machines can be encoded as multi-head pushdown automata, giving uniform and optimal under approximation algorithms modulo bounded languages.
25 citations
TL;DR: A device is presented which has its memory organized as a linear list, a type of storage equivalent to having two pushdown stores, and the nondeterministic automaton which results when the input is read one-way and the device operates in real-time.
Abstract: A device is presented which has its memory organized as a linear list, a type of storage equivalent to having two pushdown stores. Attention is then focused on the nondeterministic automaton (called an lsa) which results when the input is read one-way and the device operates in real-time. The set of words (called a language) accepted by an lsa is extensively studied. In particular, several characterizations and closure properties of languages are given.
25 citations
TL;DR: A practical technique to compile pattern-matching for prioritised overlapping patterns in equational languages into a minimal, deterministic, left-to-right, matching automaton, thereby improving on previously known equivalent bounds for the tree automaton.
Abstract: We propose a practical technique to compile pattern-matching for prioritised overlapping patterns in equational languages into a minimal, deterministic, left-to-right, matching automaton. First, we present a method for constructing a tree matching automaton for such patterns. This allows pattern-matching to be performed without any backtracking. Space requirements are reduced by using a directed acyclic graph (dag) automaton that shares all the isomorphic subautomata which are duplicated in the tree automaton. We design an efficient method to identify such subautomata and avoid duplicating their construction while generating the dag automaton. We conclude with some easily computed bounds on the size of the automata, thereby improving on previously known equivalent bounds for the tree automaton.
25 citations
06 Jul 2015
TL;DR: In this article, it was shown that the model of dense-timed pushdown automata with timeless stack is expressively equivalent to the one of PDA with infinite stack, and that the general model obtained in this way is Turing complete.
Abstract: This paper contains two results on timed extensions of pushdown automata (PDA). As our first result we prove that the model of dense-timed PDA of Abdulla et al. Collapses: it is expressively equivalent to dense-timed PDA with timeless stack. Motivated by this result, we advocate the framework of first-order definable PDA, a specialization of PDA in sets with atoms, as the right setting to define and investigate timed extensions of PDA. The general model obtained in this way is Turing complete. As our second result we prove NEXPTIME upper complexity bound for the non-emptiness problem for an expressive subclass. As a byproduct, we obtain a tight EXPTIME complexity bound for a more restrictive subclass of PDA with timeless stack, thus subsuming the complexity bound known for dense-timed PDA.
25 citations
01 Jan 1997
TL;DR: This work introduces restarting automata with rewriting, which are acceptors on the one hand, and (special) regulated rewriting systems on the other hand.
Abstract: Motivated by natural language analysis we introduce restarting automata with rewriting. They are acceptors on the one hand, and (special) regulated rewriting systems on the other hand. The computation of a restarting automaton proceeds in cycles: in each cycle, a bounded substring of the input word is rewritten by a shorter string, and the computation restarts on the arising shorter word.
25 citations