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

@article{Pacholski2000ComplexityRF, title={Complexity Results for First-Order Two-Variable Logic with Counting}, author={Leszek M. Pacholski and Wieslaw Szwast and Lidia Tendera}, journal={SIAM J. Comput.}, year={2000}, volume={29}, pages={1083-1117} }

Let $C^2_p$ denote the class of first-order sentences with two variables and with additional quantifiers "there exists exactly (at most, at least) $i$" for $i\leq p$, and let $C^2$ be the union of $C^2_p$ taken over all integers $p$. We prove that the satisfiability problem for $C^2_1$ sentences is NEXPTIME-complete. This strengthens the results by [E. Gradel, Ph. Kolaitis, and M. Vardi, Bull. Symbolic Logic, 3 (1997), pp. 53--69], who showed that the satisfiability problem for the first-order…

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