First-Order Queries on Finite Abelian Groups
نویسندگان
چکیده
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). 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems – Computations on Discrete Structures, F.4.1 Mathematical Logic – Model theory, G.2.1 Combinatorics – Combinatorial Algorithms.
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