First-Order Queries on Finite Abelian Groups

Authors Simone Bova, Barnaby Martin

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Simone Bova
Barnaby Martin

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Simone Bova and Barnaby Martin. First-Order Queries on Finite Abelian Groups. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 41-59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


We study the computational problem of checking whether a logical sentence is true in a finite abelian group. We prove that model checking first-order sentences on finite abelian groups is fixed-parameter tractable, when parameterized by the size of the sentence. We also prove that model checking monadic second-order sentences on finite abelian groups finitely presented by integer matrices is not fixed-parameter tractable (under standard assumptions in parameterized complexity).
  • Finite Abelian Groups
  • First-Order Logic
  • Monadic Second-Order Logic


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