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On Berge Multiplication for Monotone Boolean Dualization

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Automata, Languages and Programming (ICALP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5125))

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Abstract

Given the prime CNF representation φ of a monotone Boolean function f:{0,1}n↦{0,1}, the dualization problem calls for finding the corresponding prime DNF representation ψ of f. A very simple method (called Berge multiplication [2] [Page 52–53]) works by multiplying out the clauses of φ from left to right in some order, simplifying whenever possible using the absorption law. We show that for any monotone CNF φ, Berge multiplication can be done in subexponential time, and for many interesting subclasses of monotone CNF’s such as CNF’s with bounded size, bounded degree, bounded intersection, bounded conformality, and read-once formula, it can be done in polynomial or quasi-polynomial time.

The first author is thankful for the partial support by NSF (CBET-0735910). The second and third authors thank the partial support by DIMACS, the National Science Foundation’s Center for Discrete Mathematics and Theoretical Computer Science.

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Author information

Authors and Affiliations

  1. RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway, NJ 08854-8003

    Endre Boros

  2. Max-Planck-Institut für Informatik, 66111, Saarbrücken, Germany

    Khaled Elbassioni

  3. Department of Mathematical Informatics, University of Tokyo, Tokyo, 113-8656, Japan

    Kazuhisa Makino

Authors
  1. Endre Boros
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  2. Khaled Elbassioni
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  3. Kazuhisa Makino
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Editor information

Editors and Affiliations

  1. School of Computer Science, Reykjavik University, Kringlan 1, 103, Reykjavík, Iceland

    Luca Aceto

  2. Department of Computer Science, IT-Parken, University of Aarhus, Åbogade 34, 8200, ÅrhusN, Denmark

    Ivan Damgård

  3. Department of Computer Science, University of Liverpool, Ashton Building, L69 3BX, Liverpool, UK

    Leslie Ann Goldberg

  4. School of Computer Science, Reykjavik University, Kringlan 1, 103, Reykjavik, Iceland

    Magnús M. Halldórsson

  5. Department of Computer Science, Reykjavik University, Kringlan 1, 103, Reykjavík, Iceland

    Anna Ingólfsdóttir

  6. Université de Bordeaux-1, LaBRI, 351, Cours de la Libération, 33405, Talence cedex, France

    Igor Walukiewicz

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© 2008 Springer-Verlag Berlin Heidelberg

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Boros, E., Elbassioni, K., Makino, K. (2008). On Berge Multiplication for Monotone Boolean Dualization. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70575-8_5

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  • DOI: https://doi.org/10.1007/978-3-540-70575-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70574-1

  • Online ISBN: 978-3-540-70575-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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