MCS Extraction with Sublinear Oracle Queries

Lecture Notes in Computer Science

Kullmann

Ignatiev

et al. 2019

Self Cite

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.

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

On Computing the Union of MUSes

Lecture Notes in Computer Science

Kullmann

Ignatiev

et al. 2019

Self Cite

“…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

Progress in Artificial Intelligence

Marques-Silva

2019

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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.

“…Despite this, and on the other hand motivated by the various applications and fundamental connections, several algorithms for extracting an MCS of a given CNF formula have been recently proposed [3,11,[17][18][19][20]22,24], iteratively using Boolean satisfiability (SAT) solvers as the natural choice for the underlying practical NP oracle.…”

Section: Introductionmentioning

confidence: 99%

Improving MCS Enumeration via Caching

Previti

Theory and Applications of Satisfiability Testing – SAT 2017

Järvisalo

et al. 2017

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Enumeration of minimal correction sets (MCSes) of conjunctive normal form formulas is a central and highly intractable problem in infeasibility analysis of constraint systems. Often complete enumeration of MCSes is impossible due to both high computational cost and worst-case exponential number of MCSes. In such cases partial enumeration is sought for, finding applications in various domains, including axiom pinpointing in description logics among others. In this work we propose caching as a means of further improving the practical efficiency of current MCS enumeration approaches, and show the potential of caching via an empirical evaluation.