Nonnegative Rank Measures and Monotone Algebraic Branching Programs

Authors Hervé Fournier, Guillaume Malod, Maud Szusterman, Sébastien Tavenas

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Hervé Fournier
  • Université de Paris, IMJ-PRG, CNRS, F-75013 Paris, France
Guillaume Malod
  • Université de Paris, IMJ-PRG, CNRS, F-75013 Paris, France
Maud Szusterman
  • Université de Paris, IMJ-PRG, CNRS, F-75013 Paris, France
Sébastien Tavenas
  • Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA, 73000 Chambéry, France

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Hervé Fournier, Guillaume Malod, Maud Szusterman, and Sébastien Tavenas. Nonnegative Rank Measures and Monotone Algebraic Branching Programs. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 15:1-15:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Inspired by Nisan’s characterization of noncommutative complexity (Nisan 1991), we study different notions of nonnegative rank, associated complexity measures and their link with monotone computations. In particular we answer negatively an open question of Nisan asking whether nonnegative rank characterizes monotone noncommutative complexity for algebraic branching programs. We also prove a rather tight lower bound for the computation of elementary symmetric polynomials by algebraic branching programs in the monotone setting or, equivalently, in the homogeneous syntactically multilinear setting.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algebraic complexity theory
  • Theory of computation → Complexity classes
  • Elementary symmetric polynomials
  • lower bounds


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