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oai:drops-oai.dagstuhl.de:7597 2024-03-06T10:40:42Z ddc:004 open_access

On Some Computations on Sparse Polynomials Volkovich, Ilya Derandomization Arithmetic Circuits Reconstruction In arithmetic circuit complexity the standard operations are +,x. Yet, in some scenarios exponentiation gates are considered as well. In this paper we study the question of efficiently evaluating a polynomial given an oracle access to its power. Among applications, we show that: * A reconstruction algorithm for a circuit class c can be extended to handle f^e for f in C. * There exists an efficient deterministic algorithm for factoring sparse multiquadratic polynomials. * There is a deterministic algorithm for testing a factorization of sparse polynomials, with constant individual degrees, into sparse irreducible factors. That is, testing if f = g_1 x ... x g_m when f has constant individual degrees and g_i-s are irreducible. * There is a deterministic reconstruction algorithm for multilinear depth-4 circuits with two multiplication gates. * There exists an efficient deterministic algorithm for testing whether two powers of sparse polynomials are equal. That is, f^d = g^e when f and g are sparse. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ilya Volkovich 2017 Is Part Of LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX-RANDOM.2017.48 urn:nbn:de:0030-drops-75976 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.48 eng https://creativecommons.org/licenses/by/3.0/legalcode