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Circuits, Proofs and Propositional Model Counting

Authors Sravanthi Chede , Leroy Chew , Anil Shukla

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Author Details

Sravanthi Chede
  • Indian Institute of Technology Ropar, Rupnagar, India
Leroy Chew
  • TU Wien, Austria
Anil Shukla
  • Indian Institute of Technology Ropar, Rupnagar, India

Funding

  • Chew, Leroy: This work was supported by FWF ESPRIT grant no. ESP 197.

Acknowledgements

We thank Olaf Beyersdorff, Tim Hoffmann, Luc Nicolas Spachmann for useful discussions on this topic. We also thank the anonymous reviewers for helpful suggestions on the paper.

Cite As Get BibTex

Sravanthi Chede, Leroy Chew, and Anil Shukla. Circuits, Proofs and Propositional Model Counting. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 18:1-18:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.FSTTCS.2024.18

Abstract

In this paper we present a new proof system framework CLIP (Circuit Linear Induction Proposition) for propositional model counting (#SAT). A CLIP proof firstly involves a Boolean circuit, calculating the cumulative function (or running count) of models counted up to a point, and secondly a propositional proof arguing for the correctness of the circuit. 
This concept is remarkably simple and CLIP is modular so it allows us to use existing checking formats from propositional logic, especially strong proof systems. CLIP has polynomial-size proofs for XOR-pairs which are known to require exponential-size proofs in MICE [Fichte et al., 2022]. The existence of a strong proof system that can tackle these hard problems was posed as an open problem in Beyersdorff et al. [Olaf Beyersdorff et al., 2023]. In addition, CLIP systems can p-simulate all other existing #SAT proofs systems (KCPS(#SAT) [Florent Capelli, 2019], CPOG [Bryant et al., 2023], MICE). Furthermore, CLIP has a theoretical advantage over the other #SAT proof systems in the sense that CLIP only has lower bounds from its propositional proof system or if 𝖯^#𝖯 is not contained in P/poly, which is a major open problem in circuit complexity. 
CLIP uses unrestricted circuits in its proof as compared to restricted structures used by the existing #SAT proof systems. In this way, CLIP avoids hardness or limitations due to circuit restrictions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof complexity
Keywords
  • Propositional model counting
  • Boolean circuits
  • #SAT
  • Proof Systems
  • Certified Partition Operation Graph (CPOG)

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