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An effective characterization of the alternation hierarchy in two-variable logic

Authors Andreas Krebs, Howard Straubing



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Andreas Krebs
Howard Straubing

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Andreas Krebs and Howard Straubing. An effective characterization of the alternation hierarchy in two-variable logic. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 86-98, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.FSTTCS.2012.86

Abstract

We characterize the languages in the individual levels of the quantifier alternation hierarchy of first-order logic with two variables by identities. This implies decidability of the individual levels. More generally we show that two-sided semidirect products with J as the right-hand factor preserve decidability.
Keywords
  • FO_2
  • Quantifier Alternation
  • J
  • Pseudovarities
  • Identities

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