The Complexity of First-Order and Monadic Second-Order Logic Revisited

@inproceedings{Frick2002TheCO,
  title={The Complexity of First-Order and Monadic Second-Order Logic Revisited},
  author={Markus Frick and Martin Grohe},
  booktitle={LICS},
  year={2002}
}
The model-checking problem for a logic L on a class C of structures asks whether a given L-sentence holds in a given structure in C. In this paper, we give super-exponential lower bounds for fixed-parameter tractable model-checking problems for first-order and monadic second-order logic. We show that unless PTIME= NP, the model-checking problem for monadic second-order logic on finite words is not solvable in time f(k) · p(n), for anyelementaryfunction f and any polynomial p. Herek denotes the… CONTINUE READING

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