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A Tight Karp-Lipton Collapse Result in Bounded Arithmetic

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Computer Science Logic (CSL 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5213))

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Abstract

Cook and Krajíček [9] have obtained the following Karp-Lipton result in bounded arithmetic: if the theory proves , then collapses to , and this collapse is provable in . Here we show the converse implication, thus answering an open question from [9]. We obtain this result by formalizing in a hard/easy argument of Buhrman, Chang, and Fortnow [3].

In addition, we continue the investigation of propositional proof systems using advice, initiated by Cook and Krajíček [9]. In particular, we obtain several optimal and even p-optimal proof systems using advice. We further show that these p-optimal systems are equivalent to natural extensions of Frege systems.

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Authors and Affiliations

  1. Institut für Theoretische Informatik, Leibniz Universität Hannover, Germany

    Olaf Beyersdorff

  2. Institut für Informatik, Humboldt-Universität zu Berlin, Germany

    Sebastian Müller

Authors
  1. Olaf Beyersdorff
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  2. Sebastian Müller
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Michael Kaminski Simone Martini

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Beyersdorff, O., Müller, S. (2008). A Tight Karp-Lipton Collapse Result in Bounded Arithmetic. In: Kaminski, M., Martini, S. (eds) Computer Science Logic. CSL 2008. Lecture Notes in Computer Science, vol 5213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87531-4_16

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  • DOI: https://doi.org/10.1007/978-3-540-87531-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87530-7

  • Online ISBN: 978-3-540-87531-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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