文章基本信息

标题：Identity Testing and Lower Bounds for Read-k Oblivious Algebraic Branching Programs
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作者：Matthew Anderson ; Michael A. Forbes ; Ramprasad Saptharishi 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2016
卷号：50
页码：30:1-30:25
DOI：10.4230/LIPIcs.CCC.2016.30
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
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^{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.
关键词：Algebraic Complexity; Lower Bounds; Derandomization; Polynomial Identity Testing