6533b88afe1ef96bd12e2486

RESEARCH PRODUCT

FO^2 with one transitive relation is decidable

Szwast, WieslawTendera, Lidia

subject

Data processing Computer scienceclassical decision problem two-variable first-order logic decidability computational complexityddc:004Computer 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.

10.4230/lipics.stacs.2013.317https://drops.dagstuhl.de/opus/volltexte/2013/3944/