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On a Polytime Factorization Algorithm for Multilinear Polynomials over \(\mathbb {F}_2\)

  • Pavel EmelyanovEmail author
  • Denis Ponomaryov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11077)

Abstract

In 2010, Shpilka and 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 can be factored in time cubic in the size of the polynomial given as a string. Later, we have rediscovered this result and provided a simple factorization algorithm based on computations over derivatives of multilinear 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 describe an improvement of this factorization algorithm and report on preliminary experimental analysis.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.A.P. Ershov Institute of Informatics SystemsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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