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Level Two of the quantifier alternation hierarchy over infinite words
journal contribution
posted on 2018-02-22, 13:26 authored by Manfred Kufleitner, Tobias Walter© 2017 Springer Science+Business Media, LLC 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 (Formula presented.). 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 (Formula presented.) 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
Theory of Computing SystemsVolume
62Issue
3Pages
467–480Citation
KUFLEITNER, M. and WALTER, T., 2017. Level Two of the quantifier alternation hierarchy over infinite words. Theory of Computing Systems, 62 (3), pp.467–480.Publisher
SpringerVersion
- 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/Acceptance date
2017-07-16Publication date
2017-08-04Copyright date
2018Notes
This journal article is part of the following topical collections: Computer Science Symposium in Russia. This is a post-peer-review, pre-copyedit version of an article published in Theory of Computing Systems. The final authenticated version is available online at: https://doi.org/10.1007/s00224-017-9801-xISSN
1432-4350eISSN
1433-0490Publisher version
Language
- en