Deriving minimal conflict sets by CS-trees with mark set in diagnosis from first principles

Han, Benjamin; Lee, Shie-Jue

doi:10.1109/3477.752801

Cited by 36 publications

(24 citation statements)

References 7 publications

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“…General approaches to compute all minimally inconsistent subsets of a constraints system have been proposed by [3,20]. These methods correspond to various explorations of a so-called CS-tree, which aims at enumerating all subproblems of the formula.…”

Section: Approaches For Computing All Musesmentioning

confidence: 99%

On Approaches to Explaining Infeasibility of Sets of Boolean Clauses

Grégoire

Mazure

Piette

2008

2008 20th IEEE International Conference on Tools With Artificial Intelligence

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Section: Approaches For Computing All Musesmentioning

confidence: 99%

On Approaches to Explaining Infeasibility of Sets of Boolean Clauses

Grégoire

Mazure

Piette

2008

2008 20th IEEE International Conference on Tools With Artificial Intelligence

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“…More precisely, we are going to present the SMUS and SMES problems. In contrast to finding a smallest possible subset of clauses that are unsatisfiable or equivalent to the original CNF formula, the MUS and MES problems are well studied and the algorithms for solving them are deployed in practice [11,13,30,49,63,65,67].…”

Section: Applications Of Qmaxsatmentioning

confidence: 99%

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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“…The algorithms discussed in this paper rely on an important connection between MUSes and MCSes noted in [17] and [5] and exploited in [4] and [22,23] for finding all MUSes of constraint systems. Specifically, every MUS of a formula ϕ is a minimal hitting set of the complete set of ϕ's MCSes.…”

Section: Definition 2 Given An Unsatisfiable Formula ϕ a Set Of Clausesmentioning

confidence: 99%

A branch and bound algorithm for extracting smallest minimal unsatisfiable subformulas

et al. 2008

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Explaining the causes of infeasibility of Boolean formulas has practical applications in numerous fields, such as artificial intelligence (repairing inconsistent knowledge bases), formal verification (abstraction refinement and unbounded model checking), and electronic design (diagnosing and correcting infeasibility). Minimal unsatisfiable subformulas (MUSes) provide useful insights into the causes of infeasibility. An unsatisfiable formula often has many MUSes. Based on the application domain, however, MUSes with specific properties might be of interest. In this paper, we tackle the problem of finding a smallest-cardinality MUS (SMUS) of a given formula. An SMUS provides a succinct explanation of infeasibility and is valuable for applications that are heavily affected by the size of the explanation. We present (1) a baseline algorithm for finding an SMUS, founded on earlier work for finding all MUSes, and (2) a new branch-and-bound algorithm called Digger that computes a strong lower bound on the size of an SMUS and splits the problem into more tractable subformulas in a recursive search tree. Using two benchmark 416 Constraints (2009) 14:415-442 suites, we experimentally compare Digger to the baseline algorithm and to an existing incomplete genetic algorithm approach. Digger is shown to be faster in nearly all cases. It is also able to solve far more instances within a given runtime limit than either of the other approaches.

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Deriving minimal conflict sets by CS-trees with mark set in diagnosis from first principles

Cited by 36 publications

References 7 publications

On Approaches to Explaining Infeasibility of Sets of Boolean Clauses

On Approaches to Explaining Infeasibility of Sets of Boolean Clauses

Quantified maximum satisfiability

A branch and bound algorithm for extracting smallest minimal unsatisfiable subformulas

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