# On Tackling the Limits of Resolution in SAT Solving

@inproceedings{Ignatiev2017OnTT, title={On Tackling the Limits of Resolution in SAT Solving}, author={Alexey Ignatiev and Ant{\'o}nio Morgado and Joao Marques-Silva}, booktitle={SAT}, year={2017} }

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn…

## 21 Citations

MaxSAT Resolution With the Dual Rail Encoding

- Computer ScienceAAAI
- 2018

This paper investigates the DRMaxSAT proof system, and shows that DR MaxSAT p-simulates general resolution, that AC0-Frege+PHP p-Simulates DRMax sAT, and that DRMax SAT can not p- Simulate AC0 -Frege-PHP or the cutting planes proof system.

Computing with SAT Oracles: Past, Present and Future

- Computer ScienceCiE
- 2018

An overview of the practical effectiveness of SAT solvers has motivated their use as oracles for NP, enabling new algorithms that solve an ever-increasing range of hard computational problems.

Equivalence Between Systems Stronger Than Resolution

- Mathematics, Computer ScienceSAT
- 2020

It is proved that Circular Resolution and MaxSAT Resolution with extension are polynomially equivalent proof systems, generalized to arbitrary sets of inference rules with proof constructions based on circular graphs or based on weighted clauses.

Towards a Better Understanding of (Partial Weighted) MaxSAT Proof Systems

- Computer ScienceSAT
- 2020

This paper takes a proof complexity approach to MaxSAT resolution-based proof systems and shows that the strongest system captures the recently proposed concept of Circular Proof while being conceptually simpler.

Proof Complexity and SAT Solving

- Computer ScienceHandbook of Satisfiability
- 2021

This chapter gives an overview of proof complexity and connections to SAT solving, focusing on proof systems such as resolution, Nullstellensatz, polynomial calculus, and cutting planes…

Maximum Satisfiability

- Computer Science
- 2017

This chapter provides a detailed overview of the approaches to MaxSAT solving that have in recent years been most successful in solving real-world optimization problems.

A resolution calculus for MinSAT

- MathematicsLog. J. IGPL
- 2021

It is proved that the MaxSAT resolution rule also provides a complete calculus for MinSAT if it is applied following the strategy proposed here, and an exact variable elimination algorithm is described based on that rule.

Theory and Applications of Satisfiability Testing – SAT 2017

- Computer ScienceLecture Notes in Computer Science
- 2017

This work proves that one can work with much shorter parity constraints and still get rigorous mathematical guarantees, especially when the number of models is large so that many constraints need to be added.

Horn Maximum Satisfiability: Reductions, Algorithms & Applications

- Computer ScienceArXiv
- 2017

A wide range of optimization and decision problems are either naturally formulated as MaxSAT over Horn formulas, or permit simple encodings using HornMaxSAT.

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