On Tractability of Disjoint AND-Decomposition of Boolean Formulas

  • Pavel Emelyanov
  • Denis PonomaryovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8974)


Disjoint AND-decomposition of a boolean formula means its representation as a conjunction of two (or several) formulas having disjoint sets of variables. We show that deciding AND-decomposability is intractable in general for boolean formulas given in CNF or DNF and prove tractability of computing AND-decompositions of boolean formulas given in positive DNF, Full DNF, and ANF. The results follow 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.



The first author was supported by the Russian Foundation for Humanities, grant No. 13-01-12003B. The second author was supported by the German Research Foundation within the Transregional Collaborative Research Center SFB/TRR 62 “Companion-Technology for Cognitive Technical Systems”.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute of Informatics SystemsNovosibirskRussia
  2. 2.Institute of Artificial IntelligenceUlmGermany

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