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 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 rst order sentences with two variables and with additional quantiiers \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 satissability problem for C 2 1 sentences is NEXPTIME-complete. This strengthens the results by E. Grr adel, Ph. Kolaitis and M. Vardi 15] who showed that the satissability problem for the rst order two-variable logic L 2 is NEXPTIME-complete and by E. Grr adel, M… CONTINUE READING

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