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Algorithmic issues of AND-decomposition of boolean formulas

  • Computer Algebra, Applied Logic, Circuit Synthesis
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Abstract

AND-decomposition of a boolean formula means finding two (or several) formulas such that their conjunction is equivalent to the given one. Decomposition is called disjoint if the component formulas do not have variables in common. In the paper, we show that deciding AND-decomposability is intractable for boolean formulas given in CNF or DNF and prove tractability of computing disjoint AND-decomposition components of boolean formulas given in positive DNF, Full DNF, and ANF. The latter result follows from tractability of multilinear polynomial factorization over the finite field of order 2, for which we provide a polytime factorization algorithm based on identity testing for partial derivatives of multilinear polynomials.

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Authors and Affiliations

  1. Ershov Institute of Informatics Systems, Siberian Branch, Russian Academy of Sciences, pr. Lavrentiev 6, Novosibirsk, 630090, Russia

    P. G. Emelyanov & D. K. Ponomaryov

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    P. G. Emelyanov

  3. Institut für Künstliche Intelligenz, Universität Ulm, James-Franck-Ring, O27, D-89069, Ulm, Deutschland

    D. K. Ponomaryov

Authors
  1. P. G. Emelyanov
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  2. D. K. Ponomaryov
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Correspondence to P. G. Emelyanov.

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Original Russian Text © P.G. Emelyanov, D.K. Ponomaryov, 2015, published in Programmirovanie, 2015, Vol. 41, No. 3.

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Emelyanov, P.G., Ponomaryov, D.K. Algorithmic issues of AND-decomposition of boolean formulas. Program Comput Soft 41, 162–169 (2015). https://doi.org/10.1134/S0361768815030032

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  • DOI: https://doi.org/10.1134/S0361768815030032

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