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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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23 Oct 2006
TL;DR: The problem of constructing fine automata for general safety LTL formulas was left open and it is shown that while a fine automaton cannot, in general, have the same structure as the Buchi automaton for the formula, the size of afine automaton 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 Buchi 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 automaton — 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.
19 citations
27 Mar 2009
TL;DR: It is shown that for an order-n recursion scheme, one can effectively construct a non-deterministic order- n collapsible pushdown automaton representing this set of nodes in the tree generated by the scheme at which the sentence holds.
Abstract: Higher-order recursion schemes are systems of rewrite rules on typed non-terminal symbols, which can be used to define infinite trees. The Global Modal Mu-Calculus Model Checking Problem takes as input such a recursion scheme together with a modal μ -calculus sentence and asks for a finite representation of the set of nodes in the tree generated by the scheme at which the sentence holds. Using a method that appeals to game semantics, we show that for an order-n recursion scheme, one can effectively construct a non-deterministic order-n collapsible pushdown automaton representing this set. The level of the automaton is strict in the sense that in general no non-deterministic order-(n *** 1) automaton could do likewise (assuming the requisite hierarchy theorem). The question of determinisation is left open. As a corollary we can also construct an order-n collapsible pushdown automaton representing the constructible winning region of an order-n collapsible pushdown parity game.
19 citations
TL;DR: It is shown that the suffix automaton or factor automaton of a set of strings U has at most 2Q-2 states, where Q is the number of nodes of a prefix-tree representing the strings in U, which significantly improves over [email protected]?-1, the bound given by Blumer et al.
19 citations
TL;DR: The monadic depth measure is introduced which is also shown to give rise to an infinite hierarchy of language families and it is shown that the monadic hierarchy is shifted by at most one level from the unrestricted depth hierarchy.
19 citations
TL;DR: More efficient constructions for the Kleene star and for the reversal, which yield 2 ( n log n ) states, as well as an m 2 -state construction for the concatenation, are presented.
19 citations