Noise threshold for universality of 2-input gates
Information Theory
2008-09-06 v2 Computational Complexity
math.IT
Abstract
Evans and Pippenger showed in 1998 that noisy gates with 2 inputs are universal for arbitrary computation (i.e. can compute any function with bounded error), if all gates fail independently with probability epsilon and epsilon<theta, where theta is roughly 8.856%. We show that formulas built from gates with 2 inputs, in which each gate fails with probability at least theta cannot be universal. Hence, there is a threshold on the tolerable noise for formulas with 2-input gates and it is theta. We conjecture that the same threshold also holds for circuits.
Cite
@article{arxiv.0711.0351,
title = {Noise threshold for universality of 2-input gates},
author = {Falk Unger},
journal= {arXiv preprint arXiv:0711.0351},
year = {2008}
}
Comments
International Symposium on Information Theory, 2007, minor corrections in v2