eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-05-19
30:1
30:25
10.4230/LIPIcs.CCC.2016.30
article
Identity Testing and Lower Bounds for Read-k Oblivious Algebraic Branching Programs
Anderson, Matthew
Forbes, Michael A.
Saptharishi, Ramprasad
Shpilka, Amir
Volk, Ben Lee
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^{~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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol050-ccc2016/LIPIcs.CCC.2016.30/LIPIcs.CCC.2016.30.pdf
Algebraic Complexity
Lower Bounds
Derandomization
Polynomial Identity Testing