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Complexity Results for First-Order Two-Variable Logic with Counting

2000
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SIAM journal on computing (Print)
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Let C 2 p denote the class of rst order sentences with two variables and with additional quanti ers \there exists exactly (at most, at least) i", for i p, and let C 2 be the union of C 2 p taken over all integers p. We prove that the satis ability problem for C 2 1 sentences is NEXPTIME-complete. This strengthens the results by E. Gr adel, Ph. Kolaitis and M. Vardi 15] who showed that the satis ability problem for the rst order two-variable logic L 2 is NEXPTIME-complete and by E. Gr adel, M.

doi:10.1137/s0097539797323005
fatcat:zdgkvn3wefbxvanmwopwyu7a3y