Tunable Online MUS/MSS Enumeration

Authors Jaroslav Bendík, Nikola Benes, Ivana Cerná, Jirí Barnat

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Jaroslav Bendík
Nikola Benes
Ivana Cerná
Jirí Barnat

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Jaroslav Bendík, Nikola Benes, Ivana Cerná, and Jirí Barnat. Tunable Online MUS/MSS Enumeration. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 50:1-50:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


In various areas of computer science, the problem of dealing with a set of constraints arises. If the set of constraints is unsatisfiable, one may ask for a minimal description of the reason for this unsatisifiability. Minimal unsatisfiable subsets (MUSes) and maximal satisfiable subsets (MSSes) are two kinds of such minimal descriptions. The goal of this work is the enumeration of MUSes and MSSes for a given constraint system. As such full enumeration may be intractable in general, we focus on building an online algorithm, which produces MUSes/MSSes in an on-the-fly manner as soon as they are discovered. The problem has been studied before even in its online version. However, our algorithm uses a novel approach that is able to outperform the current state-of-the art algorithms for online MUS/MSS enumeration. Moreover, the performance of our algorithm can be adjusted using tunable parameters. We evaluate the algorithm on a set of benchmarks.
  • Minimal unsatisfiable subsets
  • Maximal satisfiable subsets
  • Unsatisfiab- ility analysis
  • Infeasibility analysis


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