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The VLDB Journal — The International Journal on Very Large Data Bases
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Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
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FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
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ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
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MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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ICDT'07 Proceedings of the 11th international conference on Database Theory
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DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
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MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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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 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.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.