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Exponential Separation Between Powers of Regular and General Resolution over Parities

Authors Sreejata Kishor Bhattacharya, Arkadev Chattopadhyay, Pavel Dvořák

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ACM Subject Classification
  • Theory of computation → Proof complexity
Keywords
  • Proof Complexity
  • Regular Reslin
  • Branching Programs
  • Lifting

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Abstract

Proving super-polynomial lower bounds on the size of proofs of unsatisfiability of Boolean formulas using resolution over parities is an outstanding problem that has received a lot of attention after its introduction by Itsykson and Sokolov [Dmitry Itsykson and Dmitry Sokolov, 2014]. Very recently, Efremenko, Garlík and Itsykson [Klim Efremenko et al., 2023] proved the first exponential lower bounds on the size of ResLin proofs that were additionally restricted to be bottom-regular. We show that there are formulas for which such regular ResLin proofs of unsatisfiability continue to have exponential size even though there exist short proofs of their unsatisfiability in ordinary, non-regular resolution. This is the first super-polynomial separation between the power of general ResLin and that of regular ResLin for any natural notion of regularity. 
Our argument, while building upon the work of Efremenko et al. [Klim Efremenko et al., 2023], uses additional ideas from the literature on lifting theorems.

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Sreejata Kishor Bhattacharya, Arkadev Chattopadhyay, and Pavel Dvořák. Exponential Separation Between Powers of Regular and General Resolution over Parities. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 23:1-23:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CCC.2024.23

Author Details

Sreejata Kishor Bhattacharya
  • Tata Institute of Fundamental Research, Mumbai, India
Arkadev Chattopadhyay
  • Tata Institute of Fundamental Research, Mumbai, India
Pavel Dvořák
  • Tata Institute of Fundamental Research, Mumbai, India
  • Charles University, Prague, Czech Republic

Funding

  • Chattopadhyay, Arkadev: Partially funded by the Department of Atomic Energy and a Google India Research Award.
  • Dvořák, Pavel: Work done entirely at TIFR. Supported by Czech Science Foundation GAČR grant #22-14872O.

References

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