m-sophistication
Computational Complexity
2010-01-27 v1
Abstract
The m-sophistication of a finite binary string x is introduced as a generalization of some parameter in the proof that complexity of complexity is rare. A probabilistic near sufficient statistic of x is given which length is upper bounded by the m-sophistication of x within small additive terms. This shows that m-sophistication is lower bounded by coarse sophistication and upper bounded by sophistication within small additive terms. It is also shown that m-sophistication and coarse sophistication can not be approximated by an upper or lower semicomputable function, not even within very large error.
Cite
@article{arxiv.1001.4687,
title = {m-sophistication},
author = {Bruno Bauwens},
journal= {arXiv preprint arXiv:1001.4687},
year = {2010}
}
Comments
13 pages, draft