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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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TL;DR: In this article, the authors present an alternate, simpler simulation algorithm which involves consideration only of the configurations actually reached by the automaton, which can be expected to run faster and use less storage (depending on the data structures used).
21 citations
TL;DR: This paper considers pushdown automata and exhibits exhaustive sets of upper and lower bounds on the relative succinctness of these features for three classes of languages: deterministic context-free, regular, and finite.
Abstract: This is the second in a series of papers on the inherent power of bounded cooperative concurrency, whereby an automaton can be in some bounded number of states that cooperate in accepting the input. In this paper, we consider pushdown automata. We are interested in differences in power of expression and in exponential (or higher) discrepancies in succinctness between variants of pda's that incorporate nondeterminism (E), pure parallelism (A), and bounded cooperative concurrency (C). Technically, the results are proved for cooperating push-down automata with cooperating states, but they hold for appropriate versions of most concurrent models of computation. We exhibit exhaustive sets of upper and lower bounds on the relative succinctness of these features for three classes of languages: deterministic context-free, regular, and finite. For example, we show that C represents exponential savings in succinctness in all cases except when both E and A are present (i.e., except for alternating automata), and that E and A represent unlimited savings in succinctness in all cases.
21 citations
01 Jan 2004
TL;DR: In this paper, the authors explore and compare various conditions on sets of states of which are related to the fact that induced subautomata of accept the whole language L. The methods of several previous works on minimalizations of NFA can be modified so that they fit in their approach.
Abstract: As is well known, each minimal NFA for a regular language L is isomorphic to a subautomaton of the so-called universal automaton for L. We explore and compare various conditions on sets of states of which are related to the fact that induced subautomata of accept the whole language L. The methods of several previous works on minimalizations of NFA can be modified so that they fit in our approach. We also propose a new algorithm which is easy to implement.
21 citations
Journal Article•
TL;DR: The problem of constructing fine automata for general safety LTL formulas was left open by Kupferman and Vardi as mentioned in this paper, who showed that while a fine automaton cannot, in general, have the same structure as the Buchi automaton for the formula, the size of the fine automaion is still only exponential in the length of the formula.
Abstract: Of special interest in formal verification are safety properties, which assert that the system always stays within some allowed region. Each safety property ψ can be associated with a set of bad prefixes: a set of finite computations such that an infinite computation violates ψ iff it has a prefix in the set. By translating a safety property to an automaton for its set of bad prefixes, verification can be reduced to reasoning about finite words: a system is correct if none of its computations has a bad prefix. Checking the latter circumvents the need to reason about cycles and simplifies significantly methods like symbolic fixed-point based verification, bounded model checking, and more. A drawback of the translation lies in the size of the automata: while the translation of a safety LTL formula ψ to a nondeterministic Biichi automaton is exponential, its translation to a tight bad-prefix automaton - one that accepts all the bad prefixes of ψ, is doubly exponential. Kupferman and Vardi showed that for the purpose of verification, one can replace the tight automaton by a fine automaion - one that accepts at least one bad prefix of each infinite computation that violates ψ. They also showed that for many safety LTL formulas, a fine automaton has the same structure as the Buchi automaton for the formula. The problem of constructing fine automata for general safety LTL formulas was left open. In this paper we solve this problem and show that while a fine automaton cannot, in general, have the same structure as the Buchi automaton for the formula, the size of a fine automaton is still only exponential in the length of the formula.
21 citations
TL;DR: It is proved that non Borel omega context free languages which are recognized by Buchi pushdown automata have a maximum degree of ambiguity, which implies that degrees of ambiguity are really not preserved by the operation of taking the omega power of a finitary context free language.
Abstract: We study the links between the topological complexity of an omega context free language and its degree of ambiguity. In particular, using known facts from classical descriptive set theory, we prove that non Borel omega context free languages which are recognized by Buchi pushdown automata have a maximum degree of ambiguity. This result implies that degrees of ambiguity are really not preserved by the operation of taking the omega power of a finitary context free language. We prove also that taking the adherence or the delta-limit of a finitary language preserves neither unambiguity nor inherent ambiguity. On the other side we show that methods used in the study of omega context free languages can also be applied to study the notion of ambiguity in infinitary rational relations accepted by Buchi 2-tape automata and we get first results in that direction.
21 citations