The complexity of facets resolved

Papadimitriou,; Wolfe, Rachel M. E.

doi:10.1109/sfcs.1985.56

Cited by 37 publications

(34 citation statements)

References 5 publications

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“…2) The model checking problem for (∃PF , TA, FMinSat) is D P -complete, where D P is the class of decision problems which can be described as the intersection of one NP problem and one co-NP problem [12] .…”

Section: Definition 4 a Logic System (T S R) Is Said To Be An Np-lmentioning

confidence: 99%

NP-Logic Systems and Model-Equivalence Reductions

Shen

Zhao²

2010

J. Comput. Sci. Technol.

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In this paper we investigate the existence of model-equivalence reduction between NP-logic systems which are logic systems with model existence in NP. It is shown that among all NP-systems with model checking problem in NP, the existentially quantified propositional logic (∃PF ) is maximal with respect to poly-time model-equivalent reduction. However, ∃PF seems not a maximal NP-system in general because there exits an NP-system with model checking problem D P -complete.

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Section: Definition 4 a Logic System (T S R) Is Said To Be An Np-lmentioning

confidence: 99%

NP-Logic Systems and Model-Equivalence Reductions

Shen

Zhao²

2010

J. Comput. Sci. Technol.

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“…In some of the earliest theoretical work related to MUSes, Papadimitriou and Wolfe [28] showed that recognizing a minimal unsatisfiable formula (i.e., is ϕ an MUS?) is D P -complete.…”

Section: Previous Workmentioning

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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“…Indeed, checking whether a set of clauses is a MUS or not is DP-complete [26], and checking whether a formula belongs to the set of MUSes of an unsatisfiable instance or not, is in p 2 [10]. Moreover, the number of MUSes can be exponential in the size of the instance.…”

Section: Computational Complexity and Related Workmentioning

confidence: 99%

Local-search Extraction of MUSes

2007

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SAT is probably one of the most-studied constraint satisfaction problems. In this paper, a new hybrid technique based on local search is introduced in order to approximate and extract minimally unsatisfiable subformulas (in short, MUSes) of unsatisfiable SAT instances. It is based on an original counting heuristic grafted to a local search algorithm, which explores the neighborhood of the current interpretation in an original manner, making use of a critical clause concept. Intuitively, a critical clause is a falsified clause that becomes true thanks to a local search flip only when some other clauses become f alse at the same time. In the paper, the critical clause concept is investigated. It is shown to be the cornerstone of the efficiency of our approach, which outperforms competing ones to compute MUSes, inconsistent covers and sets of MUSes, most of the time.

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The complexity of facets resolved

Cited by 37 publications

References 5 publications

NP-Logic Systems and Model-Equivalence Reductions

NP-Logic Systems and Model-Equivalence Reductions

A branch and bound algorithm for extracting smallest minimal unsatisfiable subformulas

Local-search Extraction of MUSes

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