Paper Info
Title
Identity Testing for Constant-Width, and Any-Order, Read-Once Oblivious Arithmetic Branching Programs.
Abstract
We give improved hitting sets for two special cases of Read-once Oblivious Arithmetic Branching Programs (ROABP). First is the case of an ROABP with known order of the variables. The best previously known hitting set for this case had size (nw)(O(log n)) where n is the number of variables and w is the width of the ROABP. Even for a constant-width ROABP, nothing better than a quasi-polynomial bound was known. We improve the hitting-set size for the known-order case to n(O)((log w)). In particular, this gives the first polynomial-size hitting set for constant-width ROABP (known-order). However, our hitting set only works when the characteristic of the field is zero or large enough. To construct the hitting set, we use the concept of the rank of the partial derivative matrix. Unlike previous approaches which build up from mapping variables to monomials, we map variables to polynomials directly. The second case we consider is that of polynomials computable by width-w ROABPs in any order of the variables. The best previously known hitting set for this case had size d(O(log w)) (nw)(O(log log w)) where d is the individual degree. We improve the hitting-set size to (ndw)(O(log log ) (w)).
Year
DOI
Venue
2017
10.4086/toc.2017.v013a002
THEORY OF COMPUTING
Keywords
Field
DocType
polynomial identity testing,hitting sets,arithmetic branching programs
Polynomial identity testing,Discrete mathematics,Binary logarithm,Combinatorics,Polynomial,Matrix (mathematics),Arithmetic,Partial derivative,Identity testing,Monomial,Mathematics,Branching (version control)
Journal
Volume
Issue
ISSN
13
1
1557-2862
Citations 
PageRank 
References 
0
0.34
16
Authors
3
Name
Order
Citations
PageRank
Rohit Gurjar1386.80
Arpita Korwar2293.60
Nitin Saxena328026.72