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Polynomial Identity Testing for Low Degree Polynomials with Optimal Randomness
2020
International Workshop on Approximation Algorithms for Combinatorial Optimization
We give a randomized polynomial time algorithm for polynomial identity testing for the class of n-variate poynomials of degree bounded by d over a field 𝔽, in the blackbox setting. Our algorithm works for every field 𝔽 with | 𝔽 | ≥ d+1, and uses only d log n + log (1/ ε) + O(d log log n) random bits to achieve a success probability 1 - ε for some ε > 0. In the low degree regime that is d ≪ n, it hits the information theoretic lower bound and differs from it only in the lower order terms.
doi:10.4230/lipics.approx/random.2020.8
dblp:conf/approx/BlaserP20
fatcat:soynqhsaqzgt5peas7wr52y7ia