Algebraic Characterization of the Alternation Hierarchy in FO^2[<] on Finite Words

Straubing, Howard

doi:10.4230/LIPIcs.CSL.2011.525

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Algebraic Characterization of the Alternation Hierarchy in FO^2[<] on Finite Words

Author Howard Straubing

Part of: Volume: Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (CSL 2011)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Computer Science Logic (CSL)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2011-08-31

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DOI: 10.4230/LIPIcs.CSL.2011.525
URN: urn:nbn:de:0030-drops-32549

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Keywords

automata
finite model theory

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Abstract

We give an algebraic characterization of the quantifier alternation hierarchy in first-order two-variable logic on finite words.  As a result, we obtain a new proof that this hierarchy is strict. We also show that the first two levels of the hierarchy have decidable membership problems, and conjecture an algebraic decision procedure for the other levels.

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Howard Straubing. Algebraic Characterization of the Alternation Hierarchy in FO^2[<] on Finite Words. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 525-537, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011) https://doi.org/10.4230/LIPIcs.CSL.2011.525

Author Details

Howard Straubing

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