2012 IEEE 27th Conference on Computational Complexity (2011)

San Jose, California USA

June 8, 2011 to June 11, 2011

ISSN: 1093-0159

ISBN: 978-0-7695-4411-3

pp: 273-282

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2011.18

ABSTRACT

We present a polynomial-time deterministic algorithm for testing whether constant-read multilinear arithmetic formulae are identically zero. In such a formula each variable occurs only a constant number of times and each subformula computes a multilinear polynomial. Before our work no subexponential-time deterministic algorithm was known for this class of formulae. We also present a deterministic algorithm that works in a blackbox fashion and runs in quasi-polynomial time in general, and polynomial time for constant depth. Finally, we extend our results and allow the inputs to be replaced with sparse polynomials. Our results encompass recent deterministic identity tests for sums of a constant number of read-once formulae, and for multilinear depth-four circuits.

INDEX TERMS

arithmetic circuit, bound-depth circuit, derandomization, polynomial identity testing

CITATION

Matthew Anderson,
Ilya Volkovich,
Dieter van Melkebeek,
"Derandomizing Polynomial Identity Testing for Multilinear Constant-Read Formulae",

*2012 IEEE 27th Conference on Computational Complexity*, vol. 00, no. , pp. 273-282, 2011, doi:10.1109/CCC.2011.18