Complexity of the Two-Variable Fragment with Counting Quantifiers

@article{PrattHartmann2005ComplexityOT,
  title={Complexity of the Two-Variable Fragment with Counting Quantifiers},
  author={Ian Pratt-Hartmann},
  journal={Journal of Logic, Language and Information},
  year={2005},
  volume={14},
  pages={369-395}
}
  • I. Pratt-Hartmann
  • Published 2005
  • Mathematics, Computer Science
  • Journal of Logic, Language and Information
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. 
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Complexity of the Guarded Two-variable Fragment with Counting Quantifiers
The finite satisfiability problem for the guarded two-variable fragment with counting quantifiers is in EXPTIME.
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A satisfiability preserving transformation of formulas in this fragment to the three-variable guarded fragment is given and can be computed in polynomial time and produces a formula that is linear in the size of the initial formula even for the binary coding of number restrictions. Expand
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