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Canonization for Lk-equivalence is Hard

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Computer Science Logic (CSL 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1414))

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Abstract

Let Lk be the k-variable fragment of first-order logic, for some k ≥ 3. We prove that equivalence of finite structures in Lk has no P-computable canonization function unless NP ⊑ P/poly. The latter assumption is considered as highly unlikely; in particular it implies a collapse of the polynomial hierarchy. The question for such a canonization function came up in the context of the problem of whether there is a logic for P. Slight modifications of our result yield answers to questions of Dawar, Lindell, and Weinstein [4]and Otto [16] concerning the inversion of the so-called Lk-invariants.

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Mogens Nielsen Wolfgang Thomas

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© 1998 Springer-Verlag Berlin Heidelberg

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Grohe, M. (1998). Canonization for Lk-equivalence is Hard. In: Nielsen, M., Thomas, W. (eds) Computer Science Logic. CSL 1997. Lecture Notes in Computer Science, vol 1414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028017

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  • DOI: https://doi.org/10.1007/BFb0028017

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  • Print ISBN: 978-3-540-64570-2

  • Online ISBN: 978-3-540-69353-6

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