JaCk-SAT: A New Parallel Scheme to Solve the Satisfiability Problem (SAT) Based on Join-and-Check

Many efficient algorithms for the computation of optimum stable models in the context of Answer Set Programming (ASP) are based on unsatisfiable core analysis. Among them, algorithm OLL was the first introduced in the context of ASP, whereas algorithms ONE and PMRES were first introduced for solving the Maximum Satisfiability problem (MaxSAT) and later on adapted to ASP. In this paper, we present the porting to ASP of another state-of-the-art algorithm introduced for MaxSAT, namely K, which generalizes ONE and PMRES. Moreover, we present a new algorithm called OLL-IN-ONE that compactly encodes all aggregates of OLL by taking advantage of shared aggregate sets propagators. The performance of the algorithms have been empirically compared on instances taken from the latest ASP Competition.

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Algorithms for the maximum satisfiability problem

Computing ◽

10.1007/bf02241270 ◽

1990 ◽

Vol 44 (4) ◽

pp. 279-303 ◽

Cited By ~ 192

Author(s):

Pierre Hansen ◽

Brigitte Jaumard

Keyword(s):

Satisfiability Problem ◽

Maximum Satisfiability

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GASAT: A Genetic Local Search Algorithm for the Satisfiability Problem

Evolutionary Computation ◽

10.1162/evco.2006.14.2.223 ◽

2006 ◽

Vol 14 (2) ◽

pp. 223-253 ◽

Cited By ~ 48

Author(s):

Frédéric Lardeux ◽

Frédéric Saubion ◽

Jin-Kao Hao

Keyword(s):

Tabu Search ◽

Local Search ◽

Hybrid Algorithm ◽

State Of The Art ◽

Search Algorithm ◽

Satisfiability Problem ◽

Local Search Algorithm ◽

Overall Performance ◽

Genetic Local Search ◽

Search Stage

This paper presents GASAT, a hybrid algorithm for the satisfiability problem (SAT). The main feature of GASAT is that it includes a recombination stage based on a specific crossover and a tabu search stage. We have conducted experiments to evaluate the different components of GASAT and to compare its overall performance with state-of-the-art SAT algorithms. These experiments show that GASAT provides very competitive results.

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DPLL-like satisfiability problem solver over the system of anf equations

Prikladnaya diskretnaya matematika Prilozhenie ◽

10.17223/2226308x/14/44 ◽

2021 ◽

pp. 187-190

Author(s):

A.V. Tkachev ◽

K. V. Kalgin

Keyword(s):

Satisfiability Problem ◽

Problem Solver

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Boosting branch-and-bound MaxSAT solvers with clause learning

AI Communications ◽

10.3233/aic-210178 ◽

2021 ◽

pp. 1-21

Author(s):

Chu-Min Li ◽

Zhenxing Xu ◽

Jordi Coll ◽

Felip Manyà ◽

Djamal Habet ◽

...

Keyword(s):

Experimental Investigation ◽

Combinatorial Optimization ◽

Problem Solving ◽

Branch And Bound ◽

Real World ◽

Optimization Problems ◽

Satisfiability Problem ◽

Maximum Satisfiability ◽

Combinatorial Optimization Problems ◽

Clause Learning

The Maximum Satisfiability Problem, or MaxSAT, offers a suitable problem solving formalism for combinatorial optimization problems. Nevertheless, MaxSAT solvers implementing the Branch-and-Bound (BnB) scheme have not succeeded in solving challenging real-world optimization problems. It is widely believed that BnB MaxSAT solvers are only superior on random and some specific crafted instances. At the same time, SAT-based MaxSAT solvers perform particularly well on real-world instances. To overcome this shortcoming of BnB MaxSAT solvers, this paper proposes a new BnB MaxSAT solver called MaxCDCL. The main feature of MaxCDCL is the combination of clause learning of soft conflicts and an efficient bounding procedure. Moreover, the paper reports on an experimental investigation showing that MaxCDCL is competitive when compared with the best performing solvers of the 2020 MaxSAT Evaluation. MaxCDCL performs very well on real-world instances, and solves a number of instances that other solvers cannot solve. Furthermore, MaxCDCL, when combined with the best performing MaxSAT solvers, solves the highest number of instances of a collection from all the MaxSAT evaluations held so far.

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On the Modal μ-Calculus Over Finite Symmetric Graphs

Mathematica Slovaca ◽

10.1515/ms-2015-0052 ◽

2015 ◽

Vol 65 (4) ◽

Author(s):

Giovanna D’Agostino ◽

Giacomo Lenzi

Keyword(s):

Lower Bound ◽

Upper Bound ◽

Satisfiability Problem ◽

Finite Model ◽

Model Property ◽

Finite Model Property ◽

Symmetric Graphs ◽

Trivial Consequence

AbstractIn this paper we consider the alternation hierarchy of the modal μ-calculus over finite symmetric graphs and show that in this class the hierarchy is infinite. The μ-calculus over the symmetric class does not enjoy the finite model property, hence this result is not a trivial consequence of the strictness of the hierarchy over symmetric graphs. We also find a lower bound and an upper bound for the satisfiability problem of the μ-calculus over finite symmetric graphs.

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