Comparing EQP and MOD_{p^k}P using Polynomial Degree Lower Bounds
Quantum Physics
2007-05-23 v1 Computational Complexity
Abstract
We show that an oracle A that contains either 1/4 or 3/4 of all strings of length n can be used to separate EQP from the counting classes MOD_{p^k}P. Our proof makes use of the degree of a representing polynomial over the finite field of size p^k. We show a linear lower bound on the degree of this polynomial. We also show an upper bound of O(n^{1/log_p m}) on the degree over the ring of integers modulo m, whenever m is a squarefree composite with largest prime factor p.
Cite
@article{arxiv.quant-ph/0211179,
title = {Comparing EQP and MOD_{p^k}P using Polynomial Degree Lower Bounds},
author = {M. de Graaf and P. Valiant},
journal= {arXiv preprint arXiv:quant-ph/0211179},
year = {2007}
}
Comments
10 pages, no figures