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Lower Bounds for the Weak Pigeonhole Principle Beyond Resolution

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Automata, Languages and Programming (ICALP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2076))

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Abstract

We work with an extension of Resolution, called Res(2), that allows clauses with conjunctions of two literals. In this system there are rules to introduce and eliminate such conjunctions. We prove that the weak pigeonhole principle PHP n cn and random unsatisfiable CNF formulas require exponential-size proofs in this system. This is the strongest system beyond Resolution for which such lower bounds are known. As a consequence to the result about the weak pigeonhole principle, Res(log) is exponentially more powerful than Res(2). Also we prove that Resolution cannot polynomially simulate Res(2), and that Res(2) does not have feasible monotone interpolation solving an open problem posed by Krajìček.

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Author information

Authors and Affiliations

  1. Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Barcelona

    Albert Atserias, Marìa Luisa Bonet & Juan Luis Esteban

Authors
  1. Albert Atserias
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  2. Marìa Luisa Bonet
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  3. Juan Luis Esteban
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informátics, Univ. Politècnica de Catalunya, C/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Fernando Orejas

  2. Computer Technology Institute (CTI), University of Patras, 61 Riga Feraiou street, 26221, Patras, Greece

    Paul G. Spirakis

  3. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Jan van Leeuwen

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© 2001 Springer-Verlag Berlin Heidelberg

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Atserias, A., Bonet, M.L., Esteban, J.L. (2001). Lower Bounds for the Weak Pigeonhole Principle Beyond Resolution. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_81

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  • DOI: https://doi.org/10.1007/3-540-48224-5_81

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42287-7

  • Online ISBN: 978-3-540-48224-6

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