A branch and bound algorithm for extracting smallest minimal unsatisfiable subformulas

Liffiton, Mark H.; Mneimneh, Maher; Lynce, Inês; Andraus, Zaher S.; Marques-Silva, João; Sakallah, Karem A.

doi:10.1007/s10601-008-9058-8

Cited by 32 publications

(13 citation statements)

References 30 publications

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“…Experimental results, obtained on representative problem instances, show that the core-guided QMaxSAT algorithm outperforms Digger, a state-of-the-art algorithm for the SMUS problem [45]. More importantly, these results validate the use of core-guided approaches for QMaxSAT.…”

Section: Introductionmentioning

confidence: 57%

“…A greedy genetic algorithm that finds approximate solutions of the SMUS problem was proposed in [71]. A branch and bound algorithm for computing SMUSes was described in [45,53]. The decision version of the SMUS problem, i.e.…”

Section: Definitionmentioning

confidence: 99%

“…The new algorithms for QMaxSAT are evaluated on the problems of computing the smallest minimally unsatisfiable subformula (SMUS) [29,45,49,53] and the smallest minimally equivalent subformula (SMES) [11,12,43,44]. The SMUS decision problem is well-known to be in the second level of the polynomial hierarchy (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Quantified maximum satisfiability

2015

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In recent years, there have been significant improvements in algorithms both for Quantified Boolean Formulas (QBF) and for Maximum Satisfiability (MaxSAT). This paper studies an optimization extension of QBF and considers the problem in a quantified MaxSAT setting. More precisely, the general QMaxSAT problem is defined for QBFs with a set of soft clausal constraints and consists in finding the largest subset of the soft constraints such that the remaining QBF is true. Two approaches are investigated. One is based on relaxing the soft clauses and performing an iterative search on the cost function. The other approach, which is the main contribution of the paper, is inspired by recent work on MaxSAT, and exploits the iterative identification of unsatisfiable cores. The paper investigates the application of these approaches to the two concrete problems of computing smallest minimal unsatisfiable subformulas (SMUS) and smallest minimal equivalent subformulas (SMES), decision versions of which are well-known problems in the second level of the polynomial hierarchy. Experimental results, obtained on representative problem instances, indicate that the core-guided approach for the SMUS and SMES problems outperforms the use of iterative search over the values of the cost function. More significantly, Alexey Ignatiev Constraints the core-guided approach to SMUS also outperforms the state-of-the-art SMUS extractor Digger.

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Section: Introductionmentioning

confidence: 57%

Section: Definitionmentioning

confidence: 99%

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Quantified maximum satisfiability

2015

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“…They first find the MCSes of overconstrained instances and then compute MUSes as irreducible hitting sets of the MCSes. Liffiton et al 18 has given a branch and bound algorithm for finding the smallest MUS in SAT instances. The direct approach that enumerates all the subsets of constraints and checks them for unsatisfiabilty and minimality was first reported in Ref.…”

Section: Related Workmentioning

confidence: 99%

A hybrid algorithm for finding minimal unsatisfiable subsets in over-constrained CSPs

Shah

2011

Int. J. Intell. Syst.

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Minimal Unsatisfiable Subsets (MUSes) are the subsets of constraints of an overconstrained constraint satisfaction problem (CSP) that cannot be satisfied simultaneously and therefore are responsible for the conflict in the CSP. In this paper, we present a hybrid algorithm for finding MUSes in overconstrained CSPs. The hybrid algorithm combines the direct and the indirect approaches to finding MUSes in overconstrained CSPs. Experimentation with random CSPs reveals that the hybrid approach is not only quite efficient but when operating under a time bound it finds a more representative set of MUSes. C 2011 Wiley Periodicals, Inc.

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“…In addition, there are highly optimized algorithms and off-the-shelf implementations for computing MUSes and GMUSes, such as MUSer2 [4]. Even more recent research focuses on computing a smallest (i.e., minimum-sized) MUS of a Boolean formula (SMUS) [22,1], which in general is a significantly more computationallyintensive task. Similarly, one can consider a smallest GMUS of an explicitly partitioned Boolean formula (SGMUS).…”

Section: Introductionmentioning

confidence: 99%

On computing minimal independent support and its applications to sampling and counting

et al. 2015

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Abstract. Constrained sampling and counting are two fundamental problems arising in domains ranging from artificial intelligence and security, to hardware and software testing. Recent approaches to approximate solutions for these problems rely on employing SAT solvers and universal hash functions that are typically encoded as XOR constraints of length n/2 for an input formula with n variables. As the runtime performance of SAT solvers heavily depends on the length of XOR constraints, recent research effort has been focused on reduction of length of XOR constraints. Consequently, a notion of Independent Support was proposed, and it was shown that constructing XORs over independent support (if known) can lead to a significant reduction in the length of XOR constraints without losing the theoretical guarantees of sampling and counting algorithms. In this paper, we present the first algorithmic procedure (and a corresponding tool, called MIS) to determine minimal independent support for a given CNF formula by employing a reduction to group minimal unsatisfiable subsets (GMUS). By utilizing minimal independent supports computed by MIS, we provide new tighter bounds on the length of XOR constraints for constrained counting and sampling. Furthermore, the universal hash functions constructed from independent supports computed by MIS provide two to three orders of magnitude performance improvement in state-of-the-art constrained sampling and counting tools, while still retaining theoretical guarantees.

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A branch and bound algorithm for extracting smallest minimal unsatisfiable subformulas

Cited by 32 publications

References 30 publications

Quantified maximum satisfiability

Quantified maximum satisfiability

A hybrid algorithm for finding minimal unsatisfiable subsets in over-constrained CSPs

On computing minimal independent support and its applications to sampling and counting

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