6533b858fe1ef96bd12b6d16
RESEARCH PRODUCT
FO^2 with one transitive relation is decidable
Wieslaw SzwastLidia Tenderasubject
000 Computer science knowledge general worksComputer ScienceComputer Science::Formal Languages and Automata Theorydescription
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.
year | journal | country | edition | language |
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2013-01-01 |