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Automating algebraic proof systems is NP-hard

Authors:

Susanna F. de Rezende,

Jakob Nordström,

Toniann Pitassi,

Dmitry SokolovAuthors Info & Claims

STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

Pages 209 - 222

https://doi.org/10.1145/3406325.3451080

Published: 15 June 2021 Publication History

Abstract

We show that algebraic proofs are hard to find: Given an unsatisfiable CNF formula F, it is NP-hard to find a refutation of F in the Nullstellensatz, Polynomial Calculus, or Sherali–Adams proof systems in time polynomial in the size of the shortest such refutation. Our work extends, and gives a simplified proof of, the recent breakthrough of Atserias and Müller (JACM 2020) that established an analogous result for Resolution.

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Cited By

de Rezende SLauria MNordström JSokolov D(2021)The power of negative reasoningProceedings of the 36th Computational Complexity Conference10.4230/LIPIcs.CCC.2021.40Online publication date: 20-Jul-2021
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2021.40
de Rezende S(2021)Automating Tree-Like Resolution in Time n(log ) Is ETH-HardProcedia Computer Science10.1016/j.procs.2021.11.021195:C(152-162)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1016/j.procs.2021.11.021

Index Terms

Automating algebraic proof systems is NP-hard
1. Theory of computation
  1. Computational complexity and cryptography
    1. Proof complexity

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cover image ACM Conferences

STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

June 2021

1797 pages

ISBN:9781450380539

DOI:10.1145/3406325

General Chair:
Samir Khuller
Northwestern University, USA
,
Program Chair:
Virginia Vassilevska Williams
Massachusetts Institute of Technology, USA

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Published: 15 June 2021

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STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing

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Cited By

de Rezende SLauria MNordström JSokolov D(2021)The power of negative reasoningProceedings of the 36th Computational Complexity Conference10.4230/LIPIcs.CCC.2021.40Online publication date: 20-Jul-2021
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2021.40
de Rezende S(2021)Automating Tree-Like Resolution in Time n(log ) Is ETH-HardProcedia Computer Science10.1016/j.procs.2021.11.021195:C(152-162)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1016/j.procs.2021.11.021

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