Abstract
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.
Cite
CITATION STYLE
Emelyanov, P., & Ponomaryov, D. (2015). On tractability of disjoint AND-decomposition of boolean formulas. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8974, pp. 92–101). Springer Verlag. https://doi.org/10.1007/978-3-662-46823-4_8
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