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DOI: 10.4230/LIPIcs.SAT.2025.7

Redundancy Rules for MaxSAT

Authors: Ilario Bonacina, Maria Luisa Bonet, Sam Buss, and Massimo Lauria

Published in: LIPIcs, Volume 341, 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)

Abstract

The concept of redundancy in SAT leads to more expressive and powerful proof search techniques, e.g., able to express various inprocessing techniques, and originates interesting hierarchies of proof systems [Heule et.al'20, Buss-Thapen'19]. Redundancy has also been integrated in MaxSAT [Ihalainen et.al'22, Berg et.al'23, Bonacina et.al'24]. In this paper, we define a structured hierarchy of redundancy proof systems for MaxSAT, with the goal of studying its proof complexity. We obtain MaxSAT variants of proof systems such as SPR, PR, SR, and others, previously defined for SAT. All our rules are polynomially checkable, unlike [Ihalainen et.al'22]. Moreover, they are simpler and weaker than [Berg et.al'23], and possibly amenable to lower bounds. This work also complements the approach of [Bonacina et.al'24]. Their proof systems use different rule sets for soft and hard clauses, while here we propose a system using only hard clauses and blocking variables. This is easier to integrate with current solvers and proof checkers. We discuss the strength of the systems introduced, we show some limitations of them, and we give a short cost-SR proof that any assignment for the weak pigeonhole principle PHP^m_n falsifies at least m-n clauses.

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Ilario Bonacina, Maria Luisa Bonet, Sam Buss, and Massimo Lauria. Redundancy Rules for MaxSAT. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonacina_et_al:LIPIcs.SAT.2025.7,
  author =	{Bonacina, Ilario and Bonet, Maria Luisa and Buss, Sam and Lauria, Massimo},
  title =	{{Redundancy Rules for MaxSAT}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{7:1--7:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-381-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{341},
  editor =	{Berg, Jeremias and Nordstr\"{o}m, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.7},
  URN =		{urn:nbn:de:0030-drops-237411},
  doi =		{10.4230/LIPIcs.SAT.2025.7},
  annote =	{Keywords: MaxSAT, Redundancy Rules, Pigeonhole Principle}
}

Document

DOI: 10.4230/LIPIcs.SAT.2024.7

MaxSAT Resolution with Inclusion Redundancy

Authors: Ilario Bonacina, Maria Luisa Bonet, and Massimo Lauria

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract

Popular redundancy rules for SAT are not necessarily sound for MaxSAT. The works of [Bonacina-Bonet-Buss-Lauria'24] and [Ihalainen-Berg-Järvisalo'22] proposed ways to adapt them, but required specific encodings and more sophisticated checks during proof verification. Here, we propose a different way to adapt redundancy rules from SAT to MaxSAT. Our rules do not require specific encodings, their correctness is simpler to check, but they are slightly less expressive. However, the proposed redundancy rules, when added to MaxSAT-Resolution, are already strong enough to capture Branch-and-bound algorithms, enable short proofs of the optimal cost of notable principles (e.g., the Pigeonhole Principle and the Parity Principle), and allow to break simple symmetries (e.g., XOR-ification does not make formulas harder).

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Ilario Bonacina, Maria Luisa Bonet, and Massimo Lauria. MaxSAT Resolution with Inclusion Redundancy. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bonacina_et_al:LIPIcs.SAT.2024.7,
  author =	{Bonacina, Ilario and Bonet, Maria Luisa and Lauria, Massimo},
  title =	{{MaxSAT Resolution with Inclusion Redundancy}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.7},
  URN =		{urn:nbn:de:0030-drops-205298},
  doi =		{10.4230/LIPIcs.SAT.2024.7},
  annote =	{Keywords: MaxSAT, Redundancy, MaxSAT resolution, Branch-and-bound, Pigeonhole principle, Parity Principle}
}

Document

DOI: 10.4230/LIPIcs.SAT.2023.5

Polynomial Calculus for MaxSAT

Authors: Ilario Bonacina, Maria Luisa Bonet, and Jordi Levy

Published in: LIPIcs, Volume 271, 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

Abstract

MaxSAT is the problem of finding an assignment satisfying the maximum number of clauses in a CNF formula. We consider a natural generalization of this problem to generic sets of polynomials and propose a weighted version of Polynomial Calculus to address this problem. Weighted Polynomial Calculus is a natural generalization of MaxSAT-Resolution and weighted Resolution that manipulates polynomials with coefficients in a finite field and either weights in ℕ or ℤ. We show the soundness and completeness of these systems via an algorithmic procedure. Weighted Polynomial Calculus, with weights in ℕ and coefficients in 𝔽₂, is able to prove efficiently that Tseitin formulas on a connected graph are minimally unsatisfiable. Using weights in ℤ, it also proves efficiently that the Pigeonhole Principle is minimally unsatisfiable.

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Ilario Bonacina, Maria Luisa Bonet, and Jordi Levy. Polynomial Calculus for MaxSAT. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bonacina_et_al:LIPIcs.SAT.2023.5,
  author =	{Bonacina, Ilario and Bonet, Maria Luisa and Levy, Jordi},
  title =	{{Polynomial Calculus for MaxSAT}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-286-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{271},
  editor =	{Mahajan, Meena and Slivovsky, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2023.5},
  URN =		{urn:nbn:de:0030-drops-184670},
  doi =		{10.4230/LIPIcs.SAT.2023.5},
  annote =	{Keywords: Polynomial Calculus, MaxSAT, Proof systems, Algebraic reasoning}
}

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Documents authored by Bonet, Maria Luisa

Redundancy Rules for MaxSAT

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MaxSAT Resolution with Inclusion Redundancy

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Polynomial Calculus for MaxSAT

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