Identity Testing and Lower Bounds for Read-$k$ Oblivious Algebraic Branching Programs

Matthew Anderson; Michael A. Forbes; Ramprasad Saptharishi; Amir Shpilka; Ben Lee Volk

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arXiv · 1511.07136

Identity Testing and Lower Bounds for Read-$k$ Oblivious Algebraic Branching Programs

Matthew Anderson·Michael A. Forbes·Ramprasad Saptharishi·Amir Shpilka·Ben Lee Volk

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Abstract

Read-$k$ oblivious algebraic branching programs are a natural generalization of the well-studied model of read-once oblivious algebraic branching program (ROABPs). In this work, we give an exponential lower bound of $\exp(n/k^{O(k)})$ on the width of any read-$k$ oblivious ABP computing some explicit multilinear polynomial $f$ that is computed by a polynomial size depth-$3$ circuit. We also study the polynomial identity testing (PIT) problem for this model and obtain a white-box subexponential-time PIT algorithm. The algorithm runs in time $2^{\tilde{O}(n^{1-1/2^{k-1}})}$ and needs white box access only to know the order in which the variables appear in the ABP.

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Matthew Anderson, Michael A. Forbes, Ramprasad Saptharishi, Amir Shpilka, Ben Lee Volk. 2015-11-23. Identity Testing and Lower Bounds for Read-$k$ Oblivious Algebraic Branching Programs. https://arxiv.org/abs/1511.07136

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