Alternating automata, the weak monadic theory of the tree, and its complexity

Muller, David E.; Saoudi, A.; Schnupp, Paul E.

doi:10.1007/3-540-16761-7_77

Cited by 89 publications

(80 citation statements)

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“…Alternating automata [102] present a more radical departure from the format of Büchi automata and have attracted considerable interest in recent years. The basic idea is to allow the automaton to make a transition from one location to several successor locations that are simultaneously active.…”

Section: Theorem 7 For a Büchi Automaton B With N Locations It Is Dmentioning

confidence: 99%

Model Checking: A Tutorial Overview

Merz¹

2001

Modeling and Verification of Parallel Processes

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Abstract.We survey principles of model checking techniques for the automatic analysis of reactive systems. The use of model checking is exemplified by an analysis of the Needham-Schroeder public key protocol. We then formally define transition systems, temporal logic, ω-automata, and their relationship. Basic model checking algorithms for linear-and branching-time temporal logics are defined, followed by an introduction to symbolic model checking and partial-order reduction techniques. The paper ends with a list of references to some more advanced topics.

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Section: Theorem 7 For a Büchi Automaton B With N Locations It Is Dmentioning

confidence: 99%

Model Checking: A Tutorial Overview

Merz¹

2001

Modeling and Verification of Parallel Processes

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“…Formally introduced in [MSS86], they are known to capture regular properties of infinite trees that are both Büchi and co-Büchi-recognizable, and to be expressively complete with respect to weak monadic second order logic [Rab70] and the alternation free fragment of the modal µ-calculus [AN92]. Because of their special structure, weak alternating automata have attractive computational properties.…”

Section: Introductionmentioning

confidence: 99%

On the Weak Index Problem for Game Automata

Facchini

Murlak

Skrzypczak

2015

Logic, Language, Information, and Computation

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Abstract. Game automata are known to recognise languages arbitrarily high in both the non-deterministic and alternating Rabin-Mostowski index hierarchies. Recently it was shown that for this class both hierarchies are decidable. Here we complete the picture by showing that the weak index hierarchy is decidable as well. We also provide a procedure computing for a game automaton an equivalent weak alternating automaton with the minimal index and a quadratic number of states. As a by-product we obtain that, as for deterministic automata, the weak index and the Borel rank coincide.

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“…In the early 90s, researchers started to base the automata-theoretic approach on alternating automata [19,20]. In an alternating automaton, the transition function maps a state and a letter to a formula over the set of states, indicating by which states the suffix of the word should be accepted.…”

Section: Introductionmentioning

confidence: 99%

Alternation Removal in Büchi Automata

Boker

Kupferman

Rosenberg

2010

Automata, Languages and Programming

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Abstract. Alternating automata play a key role in the automata-theoretic approach to specification, verification, and synthesis of reactive systems. Many algorithms on alternating automata, and in particular, their nonemptiness test, involve removal of alternation: a translation of the alternating automaton to an equivalent nondeterministic one. For alternating Büchi automata, the best known translation uses the "breakpoint construction" and involves an O(3 n ) state blowup. The translation was described by Miyano and Hayashi in 1984, and is widely used since, in both theory and practice. Yet, the best known lower bound is only 2 n . In this paper we develop and present a complete picture of the problem of alternation removal in alternating Büchi automata. In the lower bound front, we show that the breakpoint construction captures the accurate essence of alternation removal, and provide a matching Ω(3 n ) lower bound. Our lower bound holds already for universal (rather than alternating) automata with an alphabet of a constant size. In the upper-bound front, we point to a class of alternating Büchi automata for which the breakpoint construction can be replaced by a simpler n2 n construction. Our class, of ordered alternating Büchi automata, strictly contains the class of very-weak alternating automata, for which an n2 n construction is known.

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Alternating automata, the weak monadic theory of the tree, and its complexity

Cited by 89 publications

References 1 publication

Model Checking: A Tutorial Overview

Model Checking: A Tutorial Overview

On the Weak Index Problem for Game Automata

Alternation Removal in Büchi Automata

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