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19
On improving MUS extraction algorithms
 In Proc. of SAT 2011
, 2011
"... Abstract. Minimally Unsatisfiable Subformulas (MUS) find a wide range of practical applications, including product configuration, knowledgebased validation, and hardware and software design and verification. MUSes also find application in recent Maximum Satisfiability algorithms and in CNF formula ..."
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Abstract. Minimally Unsatisfiable Subformulas (MUS) find a wide range of practical applications, including product configuration, knowledgebased validation, and hardware and software design and verification. MUSes also find application in recent Maximum Satisfiability algorithms and in CNF formula redundancy removal. Besides direct applications in Propositional Logic, algorithms for MUS extraction have been applied to more expressive logics. This paper proposes two algorithms for MUS extraction. The first algorithm is optimal in its class, meaning that it requires the smallest number of calls to a SAT solver. The second algorithm extends earlier work, but implements a number of new techniques. The resulting algorithms achieve significant performance gains with respect to state of the art MUS extraction algorithms.
Constraint satisfaction problems in clausal form: Autarkies and minimal unsatisfiability
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY (ECCC
, 2007
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Vivifying Propositional Clausal Formulae
"... Abstract. In this paper, we present a new way to preprocess Boolean formulae in Conjunctive Normal Form (CNF). In contrast to most of the current preprocessing techniques, our approach aims at improving the filtering power of the original clauses while producing a small number of additional and rel ..."
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Abstract. In this paper, we present a new way to preprocess Boolean formulae in Conjunctive Normal Form (CNF). In contrast to most of the current preprocessing techniques, our approach aims at improving the filtering power of the original clauses while producing a small number of additional and relevant clauses. More precisely, an incomplete redundancy check is performed on each original clauses through unit propagation, leading to either a subclause or to a new relevant one generated by the clause learning scheme. This preprocessor is empirically compared to the best existing one in terms of size reduction and the ability to improve a stateoftheart satisfiability solver. 1
Logical and Algorithmic Properties of Stable Conditional Independence
, 2008
"... The logical and algorithmic properties of stable conditional independence (CI) as an alternative structural representation of conditional independence information are investigated. We utilize recent results concerning a complete axiomatization of stable conditional independence relative to discrete ..."
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Cited by 6 (0 self)
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The logical and algorithmic properties of stable conditional independence (CI) as an alternative structural representation of conditional independence information are investigated. We utilize recent results concerning a complete axiomatization of stable conditional independence relative to discrete probability measures to derive perfect model properties of stable conditional independence structures. We show that stable CI can be interpreted as a generalization of Markov networks and establish a connection between sets of stable CI statements and propositional formulas in conjunctive normal form. Consequently, we derive that the implication problem for stable CI is coNPcomplete. Finally, we show that Boolean satisfiability (SAT) solvers can be employed to efficiently decide the implication problem and to compute concise, nonredundant representations of stable CI, even for instances involving hundreds of random variables.
Redundancy in logic II: 2CNF and Horn propositional formulae
, 2005
"... We report complexity results about redundancy of formulae in 2CNF form. We first consider the problem of checking redundancy and show some algorithms that are slightly better than the trivial one. We then analyze problems related to finding irredundant equivalent subsets (i.e.s.) of a given set. The ..."
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Cited by 5 (2 self)
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We report complexity results about redundancy of formulae in 2CNF form. We first consider the problem of checking redundancy and show some algorithms that are slightly better than the trivial one. We then analyze problems related to finding irredundant equivalent subsets (i.e.s.) of a given set. The concept of cyclicity proved to be relevant to the complexity of these problems. Some results about Horn formulae are also shown. 1
Generalizing redundancy in propositional logic: Foundations and hitting sets duality
 CoRR
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Smallest MUS Extraction with Minimal Hitting Set Dualization
"... Abstract. Minimal explanations of infeasibility are of great interest in many domains. In propositional logic, these are referred to as Minimal Unsatisfiable Subsets (MUSes). An unsatisfiable formula can have multiple MUSes, some of which provide more insights than others. Different criteria can be ..."
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Abstract. Minimal explanations of infeasibility are of great interest in many domains. In propositional logic, these are referred to as Minimal Unsatisfiable Subsets (MUSes). An unsatisfiable formula can have multiple MUSes, some of which provide more insights than others. Different criteria can be considered in order to identify a good minimal explanation. Among these, the size of an MUS is arguably one of the most intuitive. Moreover, computing the smallest MUS (SMUS) finds several practical applications that include validating the quality of the MUSes computed by MUS extractors and finding equivalent subformulae of smallest size, among others. This paper develops a novel algorithm for computing a smallest MUS, and we show that it outperforms all the previous alternatives pushing the state of the art in SMUS solving. Although described in the context of propositional logic, the presented technique can also be applied to other constraint systems. 1
Inconsistency Measurement based on Variables in Minimal Unsatisfiable Subsets
, 2012
"... Measuring inconsistency degrees of knowledge bases (KBs) provides important context information for facilitating inconsistency handling. Several semantic and syntax based measures have been proposed separately. In this paper, we propose a new way to define inconsistency measurements by combining sem ..."
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Measuring inconsistency degrees of knowledge bases (KBs) provides important context information for facilitating inconsistency handling. Several semantic and syntax based measures have been proposed separately. In this paper, we propose a new way to define inconsistency measurements by combining semantic and syntax based approaches. It is based on counting the variables of minimal unsatisfiable subsets (MUSes) and minimal correction subsets (MCSes), which leads to two equivalent inconsistency degrees, named IDMUS and IDMCS. We give the theoretical and experimental comparisons between them and two purely semanticbased inconsistency degrees: 4valued and the Quasi Classical semantics based inconsistency degrees. Moreover, the computational complexities related to our new inconsistency measurements are studied. As it turns out that computing the exact inconsistency degrees is intractable in general, we then propose and evaluate an anytime algorithm to make IDMUS and IDMCS usable in knowledge management applications. In particular, as most of syntax based measures tend to be difficult to compute in reality due to the exponential number of MUSes, our new inconsistency measures are practical because the numbers of variables in MUSes are often limited or easily to be approximated. We evaluate our approach on the DC benchmark. Our encouraging experimental results show that these new inconsistency measurements or their approximations are efficient to handle large knowledge bases and to better distinguish inconsistent knowledge bases. 1
Redundancy in logic III: Nonmononotonic reasoning
, 2005
"... We study the redundancy of circumscriptive and default theories, in particular regarding the complexity of establishing whether a given theory is redundant. 1 ..."
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We study the redundancy of circumscriptive and default theories, in particular regarding the complexity of establishing whether a given theory is redundant. 1
Logical properties of stable conditional independence
 IN PROCEEDINGS OF THE 4TH EUROPEAN WORKSHOP ON PROBABILISTIC GRAPHICAL MODELS
, 2008
"... We utilize recent results concerning a complete axiomatization of stable conditional independence (CI) relative to discrete probability measures to derive perfect model properties of stable CI structures. We show that stable CI can be interpreted as a generalization of undirected graphical models an ..."
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Cited by 1 (1 self)
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We utilize recent results concerning a complete axiomatization of stable conditional independence (CI) relative to discrete probability measures to derive perfect model properties of stable CI structures. We show that stable CI can be interpreted as a generalization of undirected graphical models and establish a connection between sets of stable CI statements and propositional formulae in conjunctive normal form. Consequently, we derive that the implication problem for stable CI is coNPcomplete. Finally, we show that SAT solvers can be employed to efficiently decide the implication problem and to compute nonredundant representations of stable CI, even for instances involving hundreds of variables.