First-Order Queries on Finite Abelian Groups
Simone Bova, Barnaby D. Martin · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 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).