Resolution for Max-SAT

Abstract. Max-SAT resolution is the adaption of the powerful SAT resolution rule for the Max-SAT problem. One of the differences between these two rules is that Max-SAT resolution adds, besides the resolvent, several compensation clauses to keep the formula's equivalency. We address in this paper the problem of reducing both the number and the size of these compensation clauses. We show that the order in which the Max-SAT resolution steps are applied on the inconsistent subsets of clauses has a direct impact on the number and the sizes of the compensation clauses added to the formula. Based on this observation, we present a new algorithm for applying Max-SAT resolution on inconsistent subsets which reduces the number and the sizes of the produced compensation clauses. We demonstrate experimentally the interest of our contribution.

Section: Max-sat Resolutionmentioning

confidence: 99%

Efficient Application of Max-SAT Resolution on Inconsistent Subsets

Abramé

Habet

2014

“…The notion of MaxSAT equivalence was implicitly defined in [7]. In this paper a MaxSAT resolution rule that preserves MaxSAT equivalence is defined, and proved complete for MaxSAT.…”

Section: Examplementioning

confidence: 99%

Improving SAT-Based Weighted MaxSAT Solvers

Ansótegui

Bonet²,

Gabàs

et al. 2012

Self Cite

Abstract. In the last few years, there has been a significant effort in designing and developing efficient Weighted MaxSAT solvers. We study in detail the WPM1 algorithm identifying some weaknesses and proposing solutions to mitigate them. Basically, WPM1 is based on iteratively calling a SAT solver and adding blocking variables and cardinality constraints to relax the unsatisfiable cores returned by the SAT solver. We firstly identify and study how to break the symmetries introduced by the blocking variables and cardinality constraints. Secondly, we study how to prioritize the discovery of higher quality cores. We present an extensive experimental investigation comparing the new algorithm with state-of-the-art solvers showing that our approach makes WPM1 much more competitive.

“…In this paper we investigate the role of the so-called cycles structures (i.e., subsets of clauses of the forml 1 ∨ l 2 ,l 1 ∨ l 3 ,l 2 ∨l 3 ) 4 in the quality of the LB. Given a cycle structure, we have two options: (i) use the cycle structure just to detect inconsistent subformulas in the underestimation component (note that a cycle structure implies a failed literal l 1 ), and (ii) replace the cycle structure with l 1 , l 1 ∨l 2 ∨l 3 ,l 1 ∨ l 2 ∨ l 3 by applying MaxSAT resolution [2,5], which amounts to activate the inference component and, at the same time, change the behaviour of the underestimation component. We first show that it is better to apply MaxSAT resolution to cycle structures occurring in inconsistent subformulas detected using unit propagation or failed literal detection.…”

Section: Introductionmentioning

confidence: 99%

Exploiting Cycle Structures in Max-SAT

Manyà²,

Mohamedou

et al. 2009

Self Cite

Abstract. We investigate the role of cycles structures (i.e., subsets of clauses of the forml1 ∨ l2,l1 ∨ l3,l2 ∨l3) in the quality of the lower bound (LB) of modern MaxSAT solvers. Given a cycle structure, we have two options: (i) use the cycle structure just to detect inconsistent subformulas in the underestimation component, and (ii) replace the cycle structure withl1, l1 ∨l2 ∨l3,l1 ∨ l2 ∨ l3 by applying MaxSAT resolution and, at the same time, change the behaviour of the underestimation component. We first show that it is better to apply MaxSAT resolution to cycle structures occurring in inconsistent subformulas detected using unit propagation or failed literal detection. We then propose a heuristic that guides the application of MaxSAT resolution to cycle structures during failed literal detection, and evaluate this heuristic by implementing it in MaxSatz, obtaining a new solver called MaxSatzc. Our experiments on weighted MaxSAT and Partial MaxSAT instances indicate that MaxSatzc substantially improves MaxSatz on many hard random, crafted and industrial instances.