Communication Dans Un Congrès Année : 2019

Nonnegative rank measures and monotone algebraic branching programs

Résumé

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.

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hal-02404630 , version 1 (11-12-2019)

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Hervé Fournier, Guillaume Malod, Maud Szusterman, Sébastien Tavenas. Nonnegative rank measures and monotone algebraic branching programs. FSTTCS, Dec 2019, Mumbai, India. pp.15:1--15:14, ⟨10.4230/LIPIcs.FSTTCS.2019.15⟩. ⟨hal-02404630⟩
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