A fast parallel algorithm to compute the rank of a matrix over an arbitrary field
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Log depth circuits for division and related problems
SIAM Journal on Computing
Algorithms for sparse rational interpolation
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Computational Complexity of Sparse Rational Interpolation
SIAM Journal on Computing
Boolean Complexity of Algebraic Interpolation Problems
CSL '88 Proceedings of the 2nd Workshop on Computer Science Logic
New NP-hard and NP-complete polynomial and integer divisibility problems
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Interpolation of sparse rational functions without knowing bounds on exponents
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
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We prove for the first time an existence of the short (polynomial size) proofs for nondivisibility of two sparse polynomials (putting thus this problem is the class NP) under the Extended Riemann Hypothesis. The divisibility problem is closely related to the problem of rational interpolation. Its computational complexity was studied in [5], [4], and [6]. We prove also, somewhat surprisingly, the problem of deciding whether a rational function given by a black box equals to a polynomial belong to the parallel class NC (see, e. g., [KR 90]), provided we know the degree of its sparse representation.