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

被引：7

作者：

Anderson, Matthew ^{[1
]}

Forbes, Michael A. ^{[2
]}

Saptharishi, Ramprasad ^{[3
]}

Shpilka, Amir ^{[3
]}

Volk, Ben Lee ^{[3
]}

机构：

[1] Union Coll, Dept Comp Sci, Schenectady, NY 12308 USA

[2] Princeton Univ, Dept Comp Sci, Princeton, NJ 08544 USA

[3] Tel Aviv Univ, Dept Comp Sci, Tel Aviv, Israel

来源：

31ST CONFERENCE ON COMPUTATIONAL COMPLEXITY (CCC 2016) | 2016年 / 50卷

关键词：

Algebraic Complexity; Lower Bounds; Derandomization; Polynomial Identity Testing; PSEUDORANDOM GENERATORS; ARITHMETIC CIRCUITS; DEPTH; 4; COMPUTATION; CHASM;

D O I：

10.4230/LIPIcs.CCC.2016.30

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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 (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 xsubexponential-time PIT algorithm. The algorithm runs in time 2 (1 1/2k-i) and needs white box access only to know the order in which the variables appear in the ABP.

引用

页数：25

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