Improving MCS Enumeration via Caching

Previti, Alessandro; Mencía, Carlos; Järvisalo, Matti; Marques-Silva, João

doi:10.1007/978-3-319-66263-3_12

Cited by 13 publications

(17 citation statements)

References 27 publications

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“…A prototype implementing the proposed algorithm was written in C++ on top of the known caching MCS enumerator mcscache proposed in [25]. In the following, the prototype is referred to as umuser.…”

Section: Resultsmentioning

confidence: 99%

“…In the following, the prototype is referred to as umuser. Among the existing alternative state-of-the-art MCS and MUS enumerators [6,24,25,26], we opted to compare the prototype against mcscache as they share the same code base and the interface to a SAT solver. The underlying SAT solver used in both tools is MiniSat 2.2 [5].…”

Section: Resultsmentioning

confidence: 99%

“…Similarly, MCS and MUS membership problems are hard for Σ P 2 , and the specification of preferences of clauses to include in MUSes and MCSes are also hard for Σ P 2 [18]. Practical evidence suggests that complete enumeration of MUSes and MCSes is often beyond the reach of existing technologies, and a practical solution is the partial enumeration of either MUSes or MCSes [1,6,19,24,25,26]. A possible drawback of these approaches is that there is no guarantee that the actual sources of inconsistency in the given context are reported.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Computing the Union of MUSes

Mencía

Kullmann

Ignatiev

et al. 2019

Lecture Notes in Computer Science

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This paper considers unsatisfiable CNF formulas and addresses the problem of computing the union of the clauses included in some minimally unsatisfiable subformula (MUS). The union of MUSes represents a useful notion in infeasibility analysis since it summarizes all the causes for the unsatisfiability of a given formula. The paper proposes a novel algorithm for this problem, developing a refined recursive enumeration of MUSes based on powerful pruning techniques. Experimental results indicate the practical suitability of the approach.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Computing the Union of MUSes

Mencía

Kullmann

Ignatiev

et al. 2019

Lecture Notes in Computer Science

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“…Note that since C is an MCS, then ν does not satisfy any clause in C. Given a MaxSAT formula φ, an optimal solution to φ corresponds to the MCS C with minimum size. Hence, if we were to enumerate all MCSs of φ (Previti et al, 2017;Grégoire et al, 2018), then we can simply select an MCS of minimum size as an optimal solution for φ. x2), ( x3 )} define the set of hard and soft clauses of a MaxSAT formula φ.…”

Section: Example 2 Consider the Following Cnf Formulasmentioning

confidence: 99%

Exact and approximate determination of the Pareto set using minimal correction subsets

Guerreiro¹,

Côrtes²,

Vanderpooten³

et al. 2022

Preprint

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Recently, it has been shown that the enumeration of Minimal Correction Subsets (MCS) of Boolean formulas allows solving Multi-Objective Boolean Optimization (MOBO) formulations. However, a major drawback of this approach is that most MCSs do not correspond to Pareto-optimal solutions. In fact, one can only know that a given MCS corresponds to a Pareto-optimal solution when all MCSs are enumerated. Moreover, if it is not possible to enumerate all MCSs, then there is no guarantee of the quality of the approximation of the Pareto frontier. This paper extends the state of the art for solving MOBO using MCSs. First, we show that it is possible to use MCS enumeration to solve MOBO problems such that each MCS necessarily corresponds to a Pareto-optimal solution. Additionally, we also propose two new algorithms that can find a (1 + ε)approximation of the Pareto frontier using MCS enumeration. Experimental results in several benchmark sets show that the newly proposed algorithms allow finding better approximations of the Pareto frontier than state-of-the-art algorithms, and with guaranteed approximation ratios.

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“…Despite the high complexity of computing MCSes, efficient algorithms exist for this task (e.g. [17,5,22,21,28,29,13,23]). In the worst case, there can be an exponential number of MUSes and MCSes [25,16].…”

Section: Preliminariesmentioning

confidence: 99%

Computing Shortest Resolution Proofs

Mencía

Marques-Silva

2019

Progress in Artificial Intelligence

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Propositional resolution is a powerful proof system for unsatisfiable propositional formulas in conjunctive normal form. Resolution proofs represent useful explanations of infeasibility, with important applications. This motivates the challenge of computing shortest resolution proofs, i.e. those with the smallest number of inference steps. This paper proposes a SAT-based approach for this problem. Concretely, the paper investigates new propositional encodings for computing shortest resolution proofs and devises a number of optimizations, including symmetry breaking, additional constraints on the structure of proofs, as well as exploiting related concepts in infeasibility analysis, such as minimal correction subsets. Experimental results show the suitability of the proposed approach.

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Improving MCS Enumeration via Caching

Cited by 13 publications

References 27 publications

On Computing the Union of MUSes

On Computing the Union of MUSes

Exact and approximate determination of the Pareto set using minimal correction subsets

Computing Shortest Resolution Proofs

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