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Proof Complexity Modulo the Polynomial Hierarchy: Understanding Alternation as a Source of Hardness

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Published:18 September 2017Publication History
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Abstract

We present and study a framework in which one can present alternation-based lower bounds on proof length in proof systems for quantified Boolean formulas. A key notion in this framework is that of proof system ensemble, which is (essentially) a sequence of proof systems where, for each, proof checking can be performed in the polynomial hierarchy. We introduce a proof system ensemble called relaxing QU-res that is based on the established proof system QU-resolution. Our main results include an exponential separation of the treelike and general versions of relaxing QU-res and an exponential lower bound for relaxing QU-res; these are analogs of classical results in propositional proof complexity.

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      • Published in

        cover image ACM Transactions on Computation Theory
        ACM Transactions on Computation Theory  Volume 9, Issue 3
        September 2017
        101 pages
        ISSN:1942-3454
        EISSN:1942-3462
        DOI:10.1145/3141878
        Issue’s Table of Contents

        Copyright © 2017 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 18 September 2017
        • Accepted: 1 April 2017
        • Revised: 1 February 2017
        • Received: 1 June 2016
        Published in toct Volume 9, Issue 3

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