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

By Howard Straubing

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

Topics: automata, finite model theory, Data processing Computer science
Publisher: LIPIcs - Leibniz International Proceedings in Informatics. Computer Science Logic (CSL\u2711) - 25th International Workshop/20th Annual Conference of the EACSL
Year: 2011
DOI identifier: 10.4230/LIPIcs.CSL.2011.525
OAI identifier: oai:drops-oai.dagstuhl.de:3254

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