Decidability in the Logic of Subsequences and Supersequences

Authors Prateek Karandikar, Philippe Schnoebelen



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Prateek Karandikar
Philippe Schnoebelen

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Prateek Karandikar and Philippe Schnoebelen. Decidability in the Logic of Subsequences and Supersequences. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 84-97, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.FSTTCS.2015.84

Abstract

We consider first-order logics of sequences ordered by the subsequence ordering, aka sequence embedding. We show that the Sigma_2 theory is undecidable, answering a question left open by Kuske. Regarding fragments with a bounded number of variables, we show that the FO^2 theory is decidable while the FO^3 theory is undecidable.
Keywords
  • subsequence
  • subword
  • logic
  • first-order logic
  • decidability
  • piecewise- testability
  • Simon’s congruence

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