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Depth-d Frege Systems Are Not Automatable Unless 𝖯 = NP

Author Theodoros Papamakarios

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Author Details

Theodoros Papamakarios
  • Department of Computer Science, University of Chicago, IL, USA

Acknowledgements

I would like to thank Alexander Razborov for numerous remarks and suggestions that greatly improved the presentation of the paper.

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Theodoros Papamakarios. Depth-d Frege Systems Are Not Automatable Unless 𝖯 = NP. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CCC.2024.22

Abstract

We show that for any integer d > 0, depth-d Frege systems are NP-hard to automate. Namely, given a set S of depth-d formulas, it is NP-hard to find a depth-d Frege refutation of S in time polynomial in the size of the shortest such refutation. This extends the result of Atserias and Müller [JACM, 2020] for the non-automatability of resolution - a depth-1 Frege system - to Frege systems of any depth d > 0.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof complexity
Keywords
  • Proof complexity
  • Automatability
  • Bounded-depth Frege

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