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Replication-Guided Enumeration of Minimal Unsatisfiable Subsets

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Principles and Practice of Constraint Programming (CP 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12333))

Abstract

In many areas of computer science, we are given an unsatisfiable Boolean formula F in CNF, i.e. a set of clauses, with the goal to identify minimal unsatisfiable subsets (MUSes) of F. The more MUSes are identified, the better insight into F’s unsatisfiability is obtained. Unfortunately, finding even a single MUS can be very time consuming since it naturally subsumes repeatedly solving the satisfiability problem, and thus a complete MUS enumeration is often practically intractable. Therefore, contemporary MUS enumeration algorithms tend to identify as many MUSes as possible within a given time limit. In this work, we present a novel MUS enumeration algorithm. Compared to existing algorithms, our algorithm is much more frugal in the number of performed satisfiability checks. Consequently, our algorithm is often able to find substantially more MUSes than contemporary algorithms.

This research was supported by ERDF “CyberSecurity, CyberCrime and Critical Information Infrastructures Center of Excellence” (No. CZ.\(02.1.01/0.0/0.0/16\_019/0000822\)).

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Notes

  1. 1.

    http://www.cril.univ-artois.fr/SAT11/.

  2. 2.

    Thus, in those benchmarks, SAT solver calls are performed almost only by the shrinking procedure (which uses glucose in our implementation).

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Authors and Affiliations

  1. Faculty of Informatics, Masaryk University, Brno, Czech Republic

    Jaroslav Bendík & Ivana Černá

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  1. Jaroslav Bendík
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  2. Ivana Černá
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Correspondence to Jaroslav Bendík .

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Editors and Affiliations

  1. Insight Centre for Data Analytics, School for Computer Science and Information Technology, University College Cork, Cork, Ireland

    Helmut Simonis

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Bendík, J., Černá, I. (2020). Replication-Guided Enumeration of Minimal Unsatisfiable Subsets. In: Simonis, H. (eds) Principles and Practice of Constraint Programming. CP 2020. Lecture Notes in Computer Science(), vol 12333. Springer, Cham. https://doi.org/10.1007/978-3-030-58475-7_3

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  • DOI: https://doi.org/10.1007/978-3-030-58475-7_3

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