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.
References
SHOWING 1-10 OF 72 REFERENCES
Maximum Satisfiability Using Core-Guided MaxSAT Resolution
- Computer ScienceAAAI
- 2014
Using compressed MAXSAT resolution, this work proposes a new core-guided solver that improves the state-of-theart, solving significantly more problems than other state-ofthe-art solvers on the industrial benchmarks used in the 2013 MAXSat Solver Evaluation.
Solving MAXSAT by Solving a Sequence of Simpler SAT Instances
- Computer ScienceCP
- 2011
This paper introduces a new MAXSAT algorithm that solves a sequence of SAT instances and can, however, require solving more SAT instances than previous approaches, which is simpler than previous methods and displays superior performance on some benchmarks.
On the interplay between proof complexity and SAT solving
- Computer ScienceSIGL
- 2015
This paper is intended as an informal and accessible survey of proof complexity for non-experts, focusing on some comparatively weak proof systems of particular interest in connection with SAT…
QMaxSAT: A Partial Max-SAT Solver
- Computer ScienceJ. Satisf. Boolean Model. Comput.
- 2012
A partial Max-SAT solver QMaxSAT is presented which uses CNF encoding of Boolean cardinality constraints and is compared to the old version 0.1 which was obtained by adapting a CDCL based SAT solver MiniSat to manage cardinalities constraints.
On Using Unsatisfiability for Solving Maximum Satisfiability
- Computer ScienceArXiv
- 2007
The efficiency of the new generation of unsatisfiability-based MaxSAT solvers becomes effectively indexed to the ability of modern SAT solvers to proving unsatisfiability and identifying unsatisfiable subformulas.
Prime implicant computation using satisfiability algorithms
- Computer ScienceProceedings Ninth IEEE International Conference on Tools with Artificial Intelligence
- 1997
Given the organization of the proposed SAT algorithm, the resulting ILP procedures implement powerful search pruning techniques, including a non-chronological backtracking search strategy, clause recording procedures and identification of necessary assignments.
Towards an Optimal CNF Encoding of Boolean Cardinality Constraints
- Computer ScienceCP
- 2005
Two novel encodings of Boolean cardinality constraints in conjunctive normal form are given, one which requires only 7n clauses and 2n auxiliary variables, and another one demanding O(n·k) clauses, but with the advantage that inconsistencies can be detected in linear time by unit propagation alone.
Exploiting the Power of mip Solvers in maxsat
- Computer ScienceSAT
- 2013
An extensive empirical evaluation of a number of maxsat solvers is presented and a previously developed hybrid approach for solving maxsat is extended, that utilizes both a sat solver and a mip solver, which is shown to be quite effective.