Model-checking problems as a basis for parameterized intractability

@article{Flum2004ModelcheckingPA,
  title={Model-checking problems as a basis for parameterized intractability},
  author={J{\"o}rg Flum and Martin Grohe},
  journal={Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.},
  year={2004},
  pages={388-397}
}
  • J. Flum, Martin Grohe
  • Published 1 February 2005
  • Computer Science
  • Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
Most parameterized complexity classes are defined in terms of a parameterized version of the Boolean satisfiability problem (the so-called weighted satisfiability problem. For example, Downey and Fellow's W-hierarchy is of this form. But there are also classes, for example, the A-hierarchy, that are more naturally characterised in terms of model-checking problems for fragments of first-order logic. R. G. Downey et al. (1998) were the first to establish a connection between the two formalisms by… 

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The complexity of first-order and monadic second-order logic revisited
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    Proceedings 17th Annual IEEE Symposium on Logic in Computer Science
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It is shown that unless PTIME=NP, the model-checking problem for monadic second-order logic on finite words is not solvable in time f(k)/spl middot/p(n), for any elementary function f and any polynomial p, and under an assumption from parameterized complexity theory.
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