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Horn Maximum Satisfiability: Reductions, Algorithms and Applications

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Book cover Progress in Artificial Intelligence (EPIA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10423))

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Abstract

Recent years have witnessed remarkable performance improvements in maximum satisfiability (MaxSAT) solvers. In practice, MaxSAT algorithms often target the most generic MaxSAT formulation, whereas dedicated solvers, which address specific subclasses of MaxSAT, have not been investigated. This paper shows that a wide range of optimization and decision problems are either naturally formulated as MaxSAT over Horn formulas, or permit simple encodings using HornMaxSAT. Furthermore, the paper also shows how linear time decision procedures for Horn formulas can be used for developing novel algorithms for the HornMaxSAT problem.

This work was supported by FCT funding of post-doctoral grants SFRH/BPD/103609/2014, SFRH/BPD/120315/2016, and LASIGE Research Unit, ref. UID/CEC/00408/2013.

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Notes

  1. 1.

    In contrast, for predicate logic and many of its specializations, Horn clauses are used ubiquitously. This includes logic programming, among many others applications.

  2. 2.

    Throughout the paper, these are referred to as MaxHS-family of MaxSAT algorithms.

  3. 3.

    This corresponds to requiring \(T\subseteq V\) to be such that \(\forall _{U\subseteq V}|U|<|T|\rightarrow \exists _{\{u,v\}\in E},\{u,v\}\cap U=\emptyset \). Throughout the paper, we will skip the mathematical representation of minimum (but also maximum) size sets.

  4. 4.

    To our best knowledge, this property of propositional encodings has not been investigated before.

  5. 5.

    SCIP and CPLEX are available, respectively, from http://scip.zib.de/ and https://www-01.ibm.com/software/commerce/optimization/cplex-optimizer/.

  6. 6.

    http://www.maxsat.udl.cat/.

  7. 7.

    Due to lack of space, details are omitted.

  8. 8.

    Any implementation of the MaxHS-family of MaxSAT algorithms, by using a CDCL SAT solver, implements a basic version of the algorithm proposed in Sect. 4.

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Authors and Affiliations

  1. LASIGE, Faculty of Science, University of Lisbon, Lisbon, Portugal

    Joao Marques-Silva, Alexey Ignatiev & Antonio Morgado

  2. ISDCT SB RAS, Irkutsk, Russia

    Alexey Ignatiev

Authors
  1. Joao Marques-Silva
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  2. Alexey Ignatiev
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  3. Antonio Morgado
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Correspondence to Joao Marques-Silva .

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Editors and Affiliations

  1. Universidade do Porto, Porto, Portugal

    Eugénio Oliveira

  2. Universidade do Porto, Porto, Portugal

    João Gama

  3. Polytechnic Institute of Porto, Porto, Portugal

    Zita Vale

  4. Universidade do Porto, Porto, Portugal

    Henrique Lopes Cardoso

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Marques-Silva, J., Ignatiev, A., Morgado, A. (2017). Horn Maximum Satisfiability: Reductions, Algorithms and Applications. In: Oliveira, E., Gama, J., Vale, Z., Lopes Cardoso, H. (eds) Progress in Artificial Intelligence. EPIA 2017. Lecture Notes in Computer Science(), vol 10423. Springer, Cham. https://doi.org/10.1007/978-3-319-65340-2_56

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