Abstract
Starting from the classification of prefix vocabulary classes in first order logic (with functions) with respect to decidability/undecidability and from Trakhtenbrots Inseparability Theorem we prove NTIME-lower bounds for every set that separates (in a certain class) the formulas with a model of bounded size (depending on the length of the formula) from the invalid formulas. The results are optimal when the lower time bound is the the same function that bounds the size of the models. We prove that his can be reached for most undecidable prefix vocabulary classes. However, for some formula classes the size of the models is larger than the length of the computations that they can describe. For these classes the inseparability results are weaker.
The proofs use reductions from bounded domino problems and interpretations among different formula classes. In the last section we use such a result to prove a nondeterministic exponential time lower bound for a simple prefix class in Presburger arithmetic.
The author is supported by the Swiss National Science Foundation.
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© 1989 Springer-Verlag Berlin Heidelberg
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Grädel, E. (1989). Size of models versus length of computations. In: Börger, E., Büning, H.K., Richter, M.M. (eds) CSL '88. CSL 1988. Lecture Notes in Computer Science, vol 385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0026298
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DOI: https://doi.org/10.1007/BFb0026298
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