A complexity measure on Büchi automata

Dana Fisman

doi:10.1007/978-3-319-30000-9_8

A complexity measure on Büchi automata

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We define a complexity measure on non-deterministic Büchi automata, based on the notion of the width of the skeleton tree introduced by Kähler and Wilke. We show that the induced hierarchy tightly correlates to the Wagner Hierarchy, a corner stone in the theory of regular ω-languages that is derived from a complexity measure on deterministic Muller automata. The relation between the hierarchies entails, for instance, that a nondeterministic Büchi automaton of width k can be translated to a deterministic parity automaton of degree at most 2k+1.

Original language	English
Title of host publication	Language and Automata Theory and Applications - 10th International Conference, LATA 2016, Proceedings
Editors	Bianca Truthe, Jan Janoušek, Adrian-Horia Dediu, Carlos Martín-Vide
Publisher	Springer Verlag
Pages	102-113
Number of pages	12
ISBN (Print)	9783319299990
DOIs	https://doi.org/10.1007/978-3-319-30000-9_8
State	Published - 1 Jan 2016
Externally published	Yes
Event	10th International Conference on Language and Automata Theory and Applications, LATA 2016 - Prague, Czech Republic Duration: 14 Mar 2016 → 18 Mar 2016

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9618
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Conference on Language and Automata Theory and Applications, LATA 2016
Country/Territory	Czech Republic
City	Prague
Period	14/03/16 → 18/03/16

Keywords

Automata and logic
Automata for system analysis and program verification
Classification of regular ω-languages

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-30000-9_8

Cite this

Fisman, D. (2016). A complexity measure on Büchi automata. In B. Truthe, J. Janoušek, A.-H. Dediu, & C. Martín-Vide (Eds.), Language and Automata Theory and Applications - 10th International Conference, LATA 2016, Proceedings (pp. 102-113). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9618). Springer Verlag. https://doi.org/10.1007/978-3-319-30000-9_8

Fisman, Dana. / A complexity measure on Büchi automata. Language and Automata Theory and Applications - 10th International Conference, LATA 2016, Proceedings. editor / Bianca Truthe ; Jan Janoušek ; Adrian-Horia Dediu ; Carlos Martín-Vide. Springer Verlag, 2016. pp. 102-113 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We define a complexity measure on non-deterministic B{\"u}chi automata, based on the notion of the width of the skeleton tree introduced by K{\"a}hler and Wilke. We show that the induced hierarchy tightly correlates to the Wagner Hierarchy, a corner stone in the theory of regular ω-languages that is derived from a complexity measure on deterministic Muller automata. The relation between the hierarchies entails, for instance, that a nondeterministic B{\"u}chi automaton of width k can be translated to a deterministic parity automaton of degree at most 2k+1.",

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Fisman, D 2016, A complexity measure on Büchi automata. in B Truthe, J Janoušek, A-H Dediu & C Martín-Vide (eds), Language and Automata Theory and Applications - 10th International Conference, LATA 2016, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9618, Springer Verlag, pp. 102-113, 10th International Conference on Language and Automata Theory and Applications, LATA 2016, Prague, Czech Republic, 14/03/16. https://doi.org/10.1007/978-3-319-30000-9_8

A complexity measure on Büchi automata. / Fisman, Dana.
Language and Automata Theory and Applications - 10th International Conference, LATA 2016, Proceedings. ed. / Bianca Truthe; Jan Janoušek; Adrian-Horia Dediu; Carlos Martín-Vide. Springer Verlag, 2016. p. 102-113 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9618).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We define a complexity measure on non-deterministic Büchi automata, based on the notion of the width of the skeleton tree introduced by Kähler and Wilke. We show that the induced hierarchy tightly correlates to the Wagner Hierarchy, a corner stone in the theory of regular ω-languages that is derived from a complexity measure on deterministic Muller automata. The relation between the hierarchies entails, for instance, that a nondeterministic Büchi automaton of width k can be translated to a deterministic parity automaton of degree at most 2k+1.

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Fisman D. A complexity measure on Büchi automata. In Truthe B, Janoušek J, Dediu AH, Martín-Vide C, editors, Language and Automata Theory and Applications - 10th International Conference, LATA 2016, Proceedings. Springer Verlag. 2016. p. 102-113. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-30000-9_8

A complexity measure on Büchi automata

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