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50
On Computing Minimum Unsatisfiable Cores
, 2003
"... Certifying the correctness of a SAT solver is straightforward for satisfiable instances of SAT. Given a ..."
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Cited by 48 (3 self)
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Certifying the correctness of a SAT solver is straightforward for satisfiable instances of SAT. Given a
On finding all minimally unsatisfiable subformulas
 in Int’l Conf. on Theory and Applications of Satisfiability Testing
, 2005
"... Abstract. Much attention has been given in recent years to the problem of ..."
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Cited by 42 (4 self)
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Abstract. Much attention has been given in recent years to the problem of
Propositional Satisfiability and Constraint Programming: a Comparative Survey
 ACM Computing Surveys
, 2006
"... Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, crossfertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms ..."
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Cited by 38 (4 self)
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Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, crossfertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms that are most successful at solving both kinds of problems. They also exhibit differences in the way they are used to state and solve problems, since SAT’s approach is in general a blackbox approach, while CP aims at being tunable and programmable. This survey overviews the two areas in a comparative way, emphasising the similarities and differences between the two and the points where we feel that one technology can benefit from ideas or experience acquired
A scalable algorithm for minimal unsatisfiable core extraction
 IN PROC. SAT’06
, 2006
"... The task of extracting an unsatisfiable core for a given Boolean formula has been finding more and more applications in recent years. The only existing approach that scales well for large realworld formulas exploits the ability of modern SAT solvers to produce resolution refutations. However, the ..."
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Cited by 32 (4 self)
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The task of extracting an unsatisfiable core for a given Boolean formula has been finding more and more applications in recent years. The only existing approach that scales well for large realworld formulas exploits the ability of modern SAT solvers to produce resolution refutations. However, the resulting unsatisfiable cores are suboptimal. We propose a new algorithm for minimal unsatisfiable core extraction, based on a deeper exploration of resolutionrefutation properties. Experimental results, confirming that the algorithm is able to find minimal unsatisfiable cores for wellknown formal verification benchmarks, are provided.
MUP: A Minimal Unsatisfiability Prover
, 2005
"... After establishing the unsatisfiability of a SAT instance encoding a typical design task, there is a practical need to identify its minimal unsatisfiable subsets, which pinpoint the reasons for the infeasibility of the design. Due to the potentially expensive computation, existing tools for the ext ..."
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Cited by 31 (0 self)
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After establishing the unsatisfiability of a SAT instance encoding a typical design task, there is a practical need to identify its minimal unsatisfiable subsets, which pinpoint the reasons for the infeasibility of the design. Due to the potentially expensive computation, existing tools for the extraction of unsatisfiable subformulas do not guarantee the minimality of the results. This paper describes a practical algorithm that decides the minimal unsatisfiability of any CNF formula through BDD manipulation. This algorithm has a worsecase complexity that is exponential only in the treewidth of the CNF formula. We provide an empirical evaluation of the algorithm, highlighting its efficiency on a set of hard problems as well as its ability to work with existing subformula extraction tools to achieve optimal results.
A Simple and Flexible Way of Computing Small Unsatisfiable Cores in SAT Modulo Theories
 IN: PROCEEDINGS OF THE 10TH INTERNATIONAL CONFERENCE ON THEORY AND APPLICATIONS OF SATISFIABILITY TESTING (SAT2007
, 2007
"... Finding small unsatisfiable cores for SAT problems has recently received a lot of interest, mostly for its applications in formal verification. Surprisingly, the same problem in the context of SAT Modulo Theories (SMT) has instead received very little attention in the literature; in particular, we ..."
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Cited by 21 (3 self)
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Finding small unsatisfiable cores for SAT problems has recently received a lot of interest, mostly for its applications in formal verification. Surprisingly, the same problem in the context of SAT Modulo Theories (SMT) has instead received very little attention in the literature; in particular, we are not aware of any work aiming at producing small unsatisfiable cores in SMT. The purpose of this paper is to start filling the gap in this area, by proposing a novel approach for computing small unsat cores in SMT. The main idea is to combine an SMT solver with an external propositional core extractor: the SMT solver produces the theory lemmas found during the search; the core extractor is then called on the boolean abstraction of the original SMT problem and of the theory lemmas. This results in an unsatisfiable core for the original SMT problem, once the remaining theory lemmas have been removed. The approach has several advantages: it is extremely simple to implement
Boosting minimal unsatisfiable core extraction
 in FMCAD, 2010
"... Abstract—A variety of tasks in formal verification require finding small or minimal unsatisfiable cores (subsets) of an unsatisfiable set of constraints. This paper proposes two algorithms for finding a minimal unsatisfiable core or, if a timeout occurs, a small nonminimal unsatisfiable core. Our ..."
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Cited by 20 (0 self)
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Abstract—A variety of tasks in formal verification require finding small or minimal unsatisfiable cores (subsets) of an unsatisfiable set of constraints. This paper proposes two algorithms for finding a minimal unsatisfiable core or, if a timeout occurs, a small nonminimal unsatisfiable core. Our algorithms can be applied to either standard clauselevel unsatisfiable core extraction or highlevel unsatisfiable core extraction, that is, an extraction of an unsatisfiable core in terms of “interesting” propositional constraints supplied by the user application. We demonstrate that one of our algorithms outperforms existing algorithms for clauselevel minimal unsatisfiable core extraction on large wellknown industrial benchmarks. We also show that our algorithms are highly scalable for the problem of highlevel minimal unsatisfiable core extraction on huge benchmarks generated by Intel’s proofbased abstraction refinement flow. In addition, we provide a comparative analysis of the impact of various algorithms on unsatisfiable core extraction. I.
Extracting MUCs from constraint networks
 In Proceedings of ECAI’06
, 2006
"... Abstract. We address the problem of extracting Minimal Unsatisfiable Cores (MUCs) from constraint networks. This computationally hard problem has a practical interest in many application domains such as configuration, planning, diagnosis, etc. Indeed, identifying one or several disjoint MUCs can hel ..."
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Cited by 18 (6 self)
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Abstract. We address the problem of extracting Minimal Unsatisfiable Cores (MUCs) from constraint networks. This computationally hard problem has a practical interest in many application domains such as configuration, planning, diagnosis, etc. Indeed, identifying one or several disjoint MUCs can help circumscribe different sources of inconsistency in order to repair a system. In this paper, we propose an original approach that involves performing successive runs of a complete backtracking search, using constraint weighting, in order to surround an inconsistent part of a network, before identifying all transition constraints belonging to a MUC using a dichotomic process. We show the effectiveness of this approach, both theoretically and experimentally. 1
Finding minimal unsatisfiable cores of declarative specifications
 In FM ’08
, 2008
"... Abstract. Declarative specifications exhibit a variety of problems, such as inadvertently overconstrained axioms and underconstrained conjectures, that are hard to diagnose with model checking and theorem proving alone. Recycling core extraction is a new coverage analysis that pinpoints an irredu ..."
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Cited by 18 (9 self)
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Abstract. Declarative specifications exhibit a variety of problems, such as inadvertently overconstrained axioms and underconstrained conjectures, that are hard to diagnose with model checking and theorem proving alone. Recycling core extraction is a new coverage analysis that pinpoints an irreducible unsatisfiable core of a declarative specification. It is based on resolution refutation proofs generated by resolution engines, such as SAT solvers and resolution theorem provers. The extraction algorithm is described, and proved correct, for a generalized specification language with a regular translation to the input logic of a resolution engine. It has been implemented for the Alloy language and evaluated on a variety of specifications, with promising results. 1
Web Explanations for Semantic Heterogeneity Discovery
 In Proceedings of ESWC
, 2004
"... Managing semantic heterogeneity is a complex task. One solution involves matching like terms to each other. We view Match as an operator that takes two graphlike structures (e.g., concept hierarchies or ontologies) and returns a mapping between the nodes of the graphs that correspond semantica ..."
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Cited by 18 (8 self)
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Managing semantic heterogeneity is a complex task. One solution involves matching like terms to each other. We view Match as an operator that takes two graphlike structures (e.g., concept hierarchies or ontologies) and returns a mapping between the nodes of the graphs that correspond semantically to each other. State of the art matching systems (e.g., COMA, Cupid) perform well for many real world applications. However, matching systems may produce mappings that may not be intuitively obvious to human users. Moreover, there are cases where matching systems do not produce a useful mapping. In order for users to trust the mappings (and thus use them), they need to understand them. Also, if a system does not provide a mapping or provides a partial mapping, users need to understand answers so that they can understand either why a mapping was not produced or why only a partial answer was produced. In this paper we describe how matching systems can explain their answers using the Inference Web (IW) infrastructure. There, SMatch, a semantic matching system, produces proofs for mappings it has discovered.