A Scalable Algorithm for Minimal Unsatisfiable Core Extraction

Dershowitz, Nachum; Hanna, Ziyad; Nadel, Alexander

doi:10.1007/11814948_5

Cited by 54 publications

(63 citation statements)

References 21 publications

(26 reference statements)

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“…Examples of pruning techniques used to reduce the number of SAT solver calls include clause set trimming (during preprocessing), clause set refinement and model rotation [13,29,28,4]. Clause set refinement [13,28] exploits the SAT solver false (or unsatisfiable) outcomes to reduce the set of clauses that need to be analyzed. This consists of removing clauses that are not included in the MUS being constructed, e.g.…”

Section: Definition 1 (Mus) M ⊆ F Is a Minimal Unsatisfiable Subformmentioning

confidence: 99%

“…Afterwards, key techniques used in MUS extraction are studied. Model rotation [28,4] is applied to MES extraction, and it is argued that clause set refinement [13,29,28] cannot be directly applied to MES extraction algorithms resulting from adapting existing MUS extraction algorithms. Next, a reduction from MES to group-MUS formulation [26,29] is developed, which enables the use of both model rotation and clause set refinement.…”

Section: Mes Extraction Algorithmsmentioning

confidence: 99%

“…Efficient MUS extraction algorithms [13,29,28] must use a number of additional techniques for reducing the number of SAT solver calls. These techniques include clause set refinement [13,28] and model rotation [28,4].…”

Section: Algorithm 1: Plain Deletion-based Mes Extractionmentioning

confidence: 99%

“…These techniques include clause set refinement [13,28] and model rotation [28,4]. The next section shows how model rotation can be used in MES extraction.…”

Section: Algorithm 1: Plain Deletion-based Mes Extractionmentioning

confidence: 99%

“…First, the paper shows that many of the existing MUS extraction algorithms can be extended to the computation of MESes. Since efficient MUS extraction uses a number of key techniques for reducing the total number of SAT solver calls -namely, clause set refinement [13,29,28] and model rotation [28,4] -this paper analyzes these techniques in the context of MES extraction. The second contribution of the paper is, then, to show that model rotation can be integrated, and, in fact, improved, in MES extraction, however clause set refinement cannot be used in MES algorithms derived from the existing MUS algorithms.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On Computing Minimal Equivalent Subformulas

Belov

Janota

Lynce

et al. 2012

Lecture Notes in Computer Science

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Abstract. A propositional formula in Conjunctive Normal Form (CNF) may contain redundant clauses -clauses whose removal from the formula does not affect the set of its models. Identification of redundant clauses is important because redundancy often leads to unnecessary computation, wasted storage, and may obscure the structure of the problem. A formula obtained by the removal of all redundant clauses from a given CNF formula F is called a Minimal Equivalent Subformula (MES) of F. This paper proposes a number of efficient algorithms and optimization techniques for the computation of MESes. Previous work on MES computation proposes a simple algorithm based on iterative application of the definition of a redundant clause, similar to the well-known deletionbased approach for the computation of Minimal Unsatisfiable Subformulas (MUSes). This paper observes that, in fact, most of the existing algorithms for the computation of MUSes can be adapted to the computation of MESes. However, some of the optimization techniques that are crucial for the performance of the state-of-the-art MUS extractors cannot be applied in the context of MES computation, and thus the resulting algorithms are often not efficient in practice. To address the problem of efficient computation of MESes, the paper develops a new class of algorithms that are based on the iterative analysis of subsets of clauses. The experimental results, obtained on representative problem instances, confirm the effectiveness of the proposed algorithms. The experimental results also reveal that many CNF instances obtained from the practical applications of SAT exhibit a large degree of redundancy.

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Section: Definition 1 (Mus) M ⊆ F Is a Minimal Unsatisfiable Subformmentioning

confidence: 99%

Section: Mes Extraction Algorithmsmentioning

confidence: 99%

Section: Algorithm 1: Plain Deletion-based Mes Extractionmentioning

confidence: 99%

“…These techniques include clause set refinement [13,28] and model rotation [28,4]. The next section shows how model rotation can be used in MES extraction.…”

Section: Algorithm 1: Plain Deletion-based Mes Extractionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On Computing Minimal Equivalent Subformulas

Belov

Janota

Lynce

et al. 2012

Lecture Notes in Computer Science

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Constraint-Based Techniques in Stochastic Local Search MaxSAT Solving

Guerreiro

Terra-Neves

Lynce

et al. 2019

Lecture Notes in Computer Science

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Integrating Topological Proofs with Model Checking to Instrument Iterative Design

Menghi

Rizzi

Bernasconi

2020

Fundamental Approaches to Software Engineering

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System development is not a linear, one-shot process. It proceeds through refinements and revisions. To support assurance that the system satisfies its requirements, it is desirable that continuous verification can be performed after each refinement or revision step. To achieve practical adoption, formal system modeling and verification must accommodate continuous verification efficiently and effectively. Our proposal to address this problem is TOrPEDO, a verification approach where models are given via Partial Kripke Structures (PKSs) and requirements are specified as Linear-time Temporal Logic (LTL) properties. PKSs support refinement, by deliberately indicating unspecified parts of the model that are later completed. We support verification in two complementary forms: via model checking and proofs. Model checking is useful to provide counterexamples, i.e., pinpoint model behaviors that violate requirements. Proofs are instead useful since they can explain why requirements are satisfied. In our work, we introduce a specific concept of proof, called topological proof (TP). A TP produces a slice of the original PKS which justifies the property satisfaction. Because models can be incomplete, TOrPEDO supports reasoning on requirements satisfaction, violation, and possible satisfaction (in the case where the satisfaction depends on unknown parts).

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A Scalable Algorithm for Minimal Unsatisfiable Core Extraction

Cited by 54 publications

References 21 publications

On Computing Minimal Equivalent Subformulas

On Computing Minimal Equivalent Subformulas

Constraint-Based Techniques in Stochastic Local Search MaxSAT Solving

Integrating Topological Proofs with Model Checking to Instrument Iterative Design

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