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2011 26th Annual IEEE Conference on Computational Complexity
Derandomizing Polynomial Identity Testing for Multilinear Constant-Read Formulae
San Jose, California USA
June 08-June 11
ISBN: 978-0-7695-4411-3
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, Dieter van Melkebeek, Ilya Volkovich, "Derandomizing Polynomial Identity Testing for Multilinear Constant-Read Formulae," ccc, pp.273-282, 2011 26th Annual IEEE Conference on Computational Complexity, 2011
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