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Maximal Falsifiability

Definitions, Algorithms, and Applications
  • Alexey Ignatiev
  • Antonio Morgado
  • Jordi Planes
  • Joao Marques-Silva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8312)

Abstract

Similarly to Maximum Satisfiability (MaxSAT), Minimum Satisfiability (MinSAT) is an optimization extension of the Boolean Satisfiability (SAT) decision problem. In recent years, both problems have been studied in terms of exact and approximation algorithms. In addition, the MaxSAT problem has been characterized in terms ofMaximal Satisfiable Subsets (MSSes) andMinimal Correction Subsets (MCSes), as well as Minimal Unsatisfiable Subsets (MUSes) and minimal hitting set dualization. However, and in contrast with MaxSAT, no such characterizations exist for MinSAT. This paper addresses this issue by casting the MinSAT problem in a more general framework. The paper studies Maximal Falsifiability, the problem of computing a subset-maximal set of clauses that can be simultaneously falsified, and shows that MinSAT corresponds to the complement of a largest subset-maximal set of simultaneously falsifiable clauses, i.e. the solution of the Maximum Falsifiability (MaxFalse) problem. Additional contributions of the paper include novel algorithms for Maximum and Maximal Falsifiability, as well as minimal hitting set dualization results for the MaxFalse problem. Moreover, the proposed algorithms are validated on practical instances.

Keywords

Vertex Cover Linear Search Minimum Vertex Cover Relaxation Variable Soft Clause 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Alexey Ignatiev
    • 1
    • 4
  • Antonio Morgado
    • 1
  • Jordi Planes
    • 3
  • Joao Marques-Silva
    • 1
    • 2
  1. 1.IST/INESC-IDLisbonPortugal
  2. 2.University College DublinIreland
  3. 3.Universitat de LleidaSpain
  4. 4.ISDCT SB RASIrkutskRussia

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