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On the Complexity of the Multiplication Method for Monotone CNF/DNF Dualization

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Algorithms – ESA 2006 (ESA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4168))

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Abstract

Given the irredundant CNF representation φ of a monotone Boolean function f:{0,1}n↦{0,1}, the dualization problem calls for finding the corresponding unique irredundant DNF representation ψ of f. The (generalized) multiplication method works by repeatedly dividing the clauses of φ into (not necessarily disjoint) groups, multiplying-out the clauses in each group, and then reducing the result by applying the absorption law. We present the first non-trivial upper-bounds on the complexity of this multiplication method. Precisely, we show that if the grouping of the clauses is done in an output-independent way, then multiplication can be performed in sub-exponential time \((n|\psi|)^{(\sqrt{|\phi|})}|\phi|^{O(log n)}\). On the other hand, multiplication can be carried-out in quasi-polynomial time poly (n,|ψ|)·|ψ|o(log|ψ|), provided that the grouping is done depending on the intermediate outputs produced during the multiplication process.

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Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Khaled M. Elbassioni

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  1. Khaled M. Elbassioni
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Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA and School of Computer Science, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Yossi Azar

  2. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

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© 2006 Springer-Verlag Berlin Heidelberg

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Elbassioni, K.M. (2006). On the Complexity of the Multiplication Method for Monotone CNF/DNF Dualization. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_32

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  • DOI: https://doi.org/10.1007/11841036_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38875-3

  • Online ISBN: 978-3-540-38876-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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