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### Paper:

TR15-184 | 21st November 2015 22:21

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

TR15-184
Authors: Matthew Anderson, Michael Forbes, Ramprasad Saptharishi, Amir Shpilka, Ben Lee Volk
Publication: 22nd November 2015 06:55
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.
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.