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2015
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Deterministic polynomial identity tests for multilinear bounded-read formulae

4 years 2 months ago
Deterministic polynomial identity tests for multilinear bounded-read formulae
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. Our algorithm runs in time sO(1) ┬ĚnkO(k) , where s denotes the size of the formula, n denotes the number of variables, and k bounds the number of occurrences of each variable. 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 time nkO(k)+O(k log n) in general, and time nkO(k2)+O(kD) for depth D. 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 formulae. Keywords. Derandomization, Identity Testing, Arithmet...
Matthew Anderson, Dieter van Melkebeek, Ilya Volko
Added 17 Apr 2016
Updated 17 Apr 2016
Type Journal
Year 2015
Where CC
Authors Matthew Anderson, Dieter van Melkebeek, Ilya Volkovich
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