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

Author Howard Straubing



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LIPIcs.CSL.2011.525.pdf
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Howard Straubing

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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

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.
Keywords
  • automata
  • finite model theory

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