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Level two of the quantifier alternation hierarchy over infinite words

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conference contribution
posted on 2018-02-23, 14:13 authored by Manfred Kufleitner, Tobias Walter
© Springer International Publishing Switzerland 2016. The study of various decision problems for logic fragments has a long history in computer science. This paper is on the membership problem for a fragment of first-order logic over infinite words; the membership problem asks for a given language whether it is definable in some fixed fragment. The alphabetic topology was introduced as part of an effective characterization of the fragment Σ 2 over infinite words. Here, Σ 2 consists of the first-order formulas with two blocks of quantifiers, starting with an existential quantifier. Its Boolean closure is ð ¹Σ 2 . Our first main result is an effective characterization of the Boolean closure of the alphabetic topology, that is, given an ω-regular language L, it is decidable whether L is a Boolean combination of open sets in the alphabetic topology. This is then used for transferring Place and Zeitoun’s recent decidability result for ð ¹Σ 2 from finite to infinite words.

Funding

This work was supported by the German Research Foundation (DFG) under grants DI 435/5-2 and DI 435/6-1.

History

School

  • Science

Department

  • Computer Science

Published in

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volume

9691

Pages

223 - 236

Citation

KUFLEITNER, M. and WALTER, T., 2016. Level two of the quantifier alternation hierarchy over infinite words. IN: Kulikov, A.S. and Woeginger, G.J. (eds.) Computer Science Theory and Applications: 11th International Computer Science Symposium in Russia (CSR 2016), St. Petersburg, Russia, June 9-13, 2016, Proceedings, Chaim: Springer, pp. 223 - 236

Publisher

© Springer

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2016

Notes

This is a pre-copyedited version of a contribution published in Computer Science Theory and Applications: 11th International Computer Science Symposium in Russia (CSR 2016) edited by Kulikov, A.S. and Woeginger, G.J. published by Springer International. The definitive authenticated version is available online via https://doi.org/10.1007/978-3-319-34171-2_17

ISBN

9783319341705

ISSN

0302-9743

eISSN

1611-3349

Book series

Lecture Notes in Theoretical Computer Science and General Issues;9691

Language

  • en

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