On the Decision Problem for Two-Variable First-Order Logic

On the Decision Problem for Two-Variable First-Order Logic (1997)

by Erich Grädel , Phokion G. Kolaitis , Moshe Y. Vardi

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Datum	Value	Source
TITLE	On the Decision Problem for Two-Variable First-Order Logic	user correction - Legacy Corrections
AUTHOR NAME	Erich Grädel	user correction
AUTHOR NAME	Phokion G. Kolaitis	user correction
AUTHOR NAME	Moshe Y. Vardi	user correction
ABSTRACT	We identify the computational complexity of the satisfiability problem for FO², the fragment of first-order logic consisting of all relational first-order sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO² has the finite-model property, which means that if an FO²-sentence is satisfiable, then it has a finite model. Moreover, Mortimer showed that every satisfiable FO²-sentence has a model whose size is at most doubly exponential in the size of the sentence. In this paper, we improve Mortimer's bound by one exponential and show that every satisfiable FO²-sentence has a model whose size is at most exponential in the size of the sentence. As a consequence, we establish that the satisfiability problem for FO² is NEXPTIME-complete.	user correction
YEAR	1997	user correction - Legacy Corrections
CITATIONS	58 found	ParsCit 1.0