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Lower bounds for bounded depth Frege proofs via Pudlák-Buss games

Published: 18 May 2010 Publication History

Abstract

We present a simple proof of the bounded-depth Frege proof lower bounds of Pitassi et al. [1993] and Krajíček et al. [1995] for the pigeonhole principle. Our method uses the interpretation of proofs as two player games given by Pudlák and Buss. Our lower bound is conceptually simpler than previous ones, and relies on tools and intuition that are well known in the context of computational complexity. This makes the lower bound of Pitassi et al. [1993] and Krajíček et al. [1995] accessible to the general computational complexity audience. We hope this new view will open new directions for research in proof complexity.

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  1. Lower bounds for bounded depth Frege proofs via Pudlák-Buss games

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    cover image ACM Transactions on Computational Logic
    ACM Transactions on Computational Logic  Volume 11, Issue 3
    May 2010
    158 pages
    ISSN:1529-3785
    EISSN:1557-945X
    DOI:10.1145/1740582
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 18 May 2010
    Accepted: 01 June 2009
    Revised: 01 June 2009
    Received: 01 June 2008
    Published in TOCL Volume 11, Issue 3

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    Author Tags

    1. Frege proofs
    2. Proof complexity
    3. lower bounds
    4. pigeonhole principle

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