Complexity of the two-variable fragment with counting quantifiers. (English) Zbl 1082.03007
Summary: The satisfiability and finite satisfiability problems for the two-variable fragment of first-order logic with counting quantifiers are both in NEXPTIME, even when counting quantifiers are coded succinctly.
MSC:
| 03B20 | Subsystems of classical logic (including intuitionistic logic) |
| 03B25 | Decidability of theories and sets of sentences |
| 03D15 | Complexity of computation (including implicit computational complexity) |
Keywords:
complexity; satisfiability; two-variable fragment of first-order logic; counting quantifiersReferences:
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| [2] | Grädel, E., Otto, M., and Rosen, E., 1997, ”Two-variable logic with counting is decidable,” in Proceedings of the 12th IEEE Symposium on Logic in Computer Science, pp. 306–317. IEEE Online Publications. |
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| [4] | Pacholski, L., Szwast, W., and Tendera, L., 1999, ”Complexity results for first-order two-variable logic with counting,” SIAM Journal on Computing 29(4), 1083–1117. · Zbl 0956.03039 · doi:10.1137/S0097539797323005 |
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