First-Order Queries on Finite Abelian Groups
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
41-59
Regular Paper
Simone
Bova
Simone Bova
Barnaby
Martin
Barnaby Martin
10.4230/LIPIcs.CSL.2015.41
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode