Complexity and real computation
Complexity and real computation
On the Structure of $\cal NP_\Bbb C$
SIAM Journal on Computing
On lower bounds for the complexity of polynomials and their multiples
Computational Complexity
On a transfer theorem for the P≠NP conjecture
Journal of Complexity
Combinatorial Hardness Proofs for Polynomial Evaluation
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
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Lower bounds for some explicit decision problems over the complex numbers are given. The decision problems considered are certain zero-dimensional subsets of NC, and can be assimilated to a countable family of polynomials gi. More precisely, one should decide for input (i,x) if gi(x)=0. A lower bound for deciding if a polynomial gi vanishes at some x can be derived from a uniform lower bound for the evaluation of all f(gi). That bound is obtained by means of an arithmetic invariant of the roots of gi, the Newton diagram of f and other known techniques.