6533b858fe1ef96bd12b6d16

RESEARCH PRODUCT

FO^2 with one transitive relation is decidable

Wieslaw SzwastLidia Tendera

subject

000 Computer science knowledge general worksComputer ScienceComputer Science::Formal Languages and Automata Theory

description

We show that the satisfiability problem for the two-variable first-order logic, FO^2, over transitive structures when only one relation is required to be transitive, is decidable. The result is optimal, as FO^2 over structures with two transitive relations, or with one transitive and one equivalence relation, are known to be undecidable, so in fact, our result completes the classification of FO^2-logics over transitive structures with respect to decidability. We show that the satisfiability problem is in 2-NExpTime. Decidability of the finite satisfiability problem remains open.

https://dx.doi.org/10.4230/lipics.stacs.2013.317