SAT encodings for Pseudo-Boolean constraints together with at-most-one constraints

Bofill, Miquel; Coll, Jordi; Nightingale, Peter; Suy, Josep; Ulrich-Oltean, Felix; Villaret, Mateu

doi:10.1016/j.artint.2021.103604

Cited by 5 publications

(1 citation statement)

References 37 publications

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“…As an illustrative example we consider the analysis of the propagation strength of a SAT encoding. We are given a SAT formula consisting of the encoding of the cardinality constraint x 1 +x 2 +x 3 +x 4 ≥3, and this encoding is supposed to maintain Generalized Arc Consistency (GAC) by UP [14]. Satisfying the GAC property implies, for instance, that assigning false to one of the three variables must make UP assign true to the other three.…”

Section: Conclusion An Future Workmentioning

confidence: 99%

SAT-IT: The Interactive SAT Tracer

Cané,

Coll,

Rojo

et al. 2023

Frontiers in Artificial Intelligence and Applications

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In this work we present the Interactive SAT Tracer (SAT-IT), a visual and interactive tool to monitor and illustrate the basic algorithms for solving the Boolean Satisfiability Problem (SAT). We consider three algorithms with progressively increasing sophistication: simple backtracking, its extension with unit-propagation, so called Davis-Putnam-Logemann-Loveland (DPLL), and its further extension with clause-learning and conflict driven, so called Conflict-Driven Clause Learning (CDCL). The motivation of this tool is to provide an environment where the user can see the full trace of a SAT solving process in a compact but detailed way and understand the reasons why each variable assignment, backtrack or back-jump occurs. Moreover, we want the user to be able to control the evolution of the solving process at the desired pace, and let they choose what branchings (or decisions) must be done. Being able to control the solving process and having detailed information of this process, results in many pedagogical and research applications such as understanding algorithms or designing encodings.

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Section: Conclusion An Future Workmentioning

confidence: 99%

SAT-IT: The Interactive SAT Tracer

Cané,

Coll,

Rojo

et al. 2023

Frontiers in Artificial Intelligence and Applications

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Learning to select SAT encodings for pseudo-Boolean and linear integer constraints

Ulrich-Oltean,

Nightingale,

Walker

2023

Constraints

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Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the literature with widely varying performance, and the problem of selecting suitable encodings for a given problem instance is not trivial. We explore the problem of selecting encodings for pseudo-Boolean and linear constraints using a supervised machine learning approach. We show that it is possible to select encodings effectively using a standard set of features for constraint problems; however we obtain better performance with a new set of features specifically designed for the pseudo-Boolean and linear constraints. In fact, we achieve good results when selecting encodings for unseen problem classes. Our results compare favourably to AutoFolio when using the same feature set. We discuss the relative importance of instance features to the task of selecting the best encodings, and compare several variations of the machine learning method.

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