Logic in Computer Science, Symposium on (2002)

Copenhagen, Denmark

July 22, 2002 to July 25, 2002

ISSN: 1043-6871

ISBN: 0-7695-1483-9

pp: 215

Martin Grohe , University of Edinburgh

Markus Frick , University of Edinburgh

ABSTRACT

<p>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.</p> <p>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 any elementary function f and any polynomial p. Here k denotes the size of the input sentence and n the size of the input word. We prove the same result for first-order logic under a stronger complexity theoretic assumption from parameterized complexity theory.</p> <p>Furthermore, we prove that the model-checking problems for first-order logic on structures of degree 2 and of bounded degree d\leqslant 3 are not solvable in time 2^(2^{0(k)}} ?p(n) (for degree 2), and 2^{2^{2^{0(k)}}} ?p(n) (for degree d) for any polynomial p, again under an assumption from parameterized complexity theory. We match these lower bounds by corresponding upper bounds.</p>

INDEX TERMS

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CITATION

Martin Grohe,
Markus Frick,
"The Complexity of First-Order and Monadic Second-Order Logic Revisited",

*Logic in Computer Science, Symposium on*, vol. 00, no. , pp. 215, 2002, doi:10.1109/LICS.2002.1029830