research-article

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

Author:

Hubie ChenAuthors Info & Claims

ACM Transactions on Computation Theory (TOCT), Volume 9, Issue 3

Article No.: 15, Pages 1 - 20

https://doi.org/10.1145/3087534

Published: 18 September 2017 Publication History

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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Cited By

Chew L(2021)Hardness and Optimality in QBF Proof Systems Modulo NPTheory and Applications of Satisfiability Testing – SAT 202110.1007/978-3-030-80223-3_8(98-115)Online publication date: 2-Jul-2021
https://doi.org/10.1007/978-3-030-80223-3_8
Beyersdorff OBlinkhorn JMahajan MHermanns HZhang LKobayashi NMiller D(2020)Hardness Characterisations and Size-Width Lower Bounds for QBF ResolutionProceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3373718.3394793(209-223)Online publication date: 8-Jul-2020
https://dl.acm.org/doi/10.1145/3373718.3394793
Beyersdorff OChew LJanota M(2019)New Resolution-Based QBF Calculi and Their Proof ComplexityACM Transactions on Computation Theory10.1145/335215511:4(1-42)Online publication date: 12-Sep-2019
https://dl.acm.org/doi/10.1145/3352155
Show More Cited By

Index Terms

Proof Complexity Modulo the Polynomial Hierarchy: Understanding Alternation as a Source of Hardness
1. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
    2. Proof complexity

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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

Editor:
Venkatesan Guruswami
Carnegie Mellon University, USA

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: 01 April 2017

Revised: 01 February 2017

Received: 01 June 2016

Published in TOCT Volume 9, Issue 3

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Basque Government Project
University of the Basque Country
Spanish Project FORMALISM

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Cited By

Chew L(2021)Hardness and Optimality in QBF Proof Systems Modulo NPTheory and Applications of Satisfiability Testing – SAT 202110.1007/978-3-030-80223-3_8(98-115)Online publication date: 2-Jul-2021
https://doi.org/10.1007/978-3-030-80223-3_8
Beyersdorff OBlinkhorn JMahajan MHermanns HZhang LKobayashi NMiller D(2020)Hardness Characterisations and Size-Width Lower Bounds for QBF ResolutionProceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3373718.3394793(209-223)Online publication date: 8-Jul-2020
https://dl.acm.org/doi/10.1145/3373718.3394793
Beyersdorff OChew LJanota M(2019)New Resolution-Based QBF Calculi and Their Proof ComplexityACM Transactions on Computation Theory10.1145/335215511:4(1-42)Online publication date: 12-Sep-2019
https://dl.acm.org/doi/10.1145/3352155
Beyersdorff OHinde L(2019)Characterising tree-like Frege proofs for QBFInformation and Computation10.1016/j.ic.2019.05.002268(104429)Online publication date: Oct-2019
https://doi.org/10.1016/j.ic.2019.05.002

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