On Polytime Algorithm for Factorization of Multilinear Polynomials Over F2

05/21/2018

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by   Pavel Emelyanov, et al.

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In 2010, A. Shpilka and I. Volkovich established a prominent result on the equivalence of polynomial factorization and identity testing. It follows from their result that a multilinear polynomial over the finite field of order 2 (a multilinear boolean polynomial) can be factored in time cubic in the size of the polynomial given as a string. We have later rediscovered this result and provided a simple factorization algorithm based on the computation of derivatives of multilinear boolean polynomials. The algorithm has been applied to solve problems of compact representation of various combinatorial structures, including boolean functions and relational data tables. In this paper, we improve the known cubic upper complexity bound of this factorization algorithm and report on a preliminary experimental analysis.