ECCC-Report TR15-184https://eccc.weizmann.ac.il/report/2015/184Comments and Revisions published for TR15-184en-usSun, 22 Nov 2015 06:55:31 +0200
Paper TR15-184
| Identity Testing and Lower Bounds for Read-$k$ Oblivious Algebraic Branching Programs |
Matthew Anderson,
Michael Forbes,
Amir Shpilka,
Ramprasad Saptharishi,
Ben Lee Volk
https://eccc.weizmann.ac.il/report/2015/184Read-$k$ 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.Sun, 22 Nov 2015 06:55:31 +0200https://eccc.weizmann.ac.il/report/2015/184