Sets Have Simple Members
Computational Complexity
2014-03-21 v9
Abstract
The combined Universal Probability M(D) of strings x in sets D is close to max M({x}) over x in D: their ~logs differ by at most D's information j=I(D:H) about the halting sequence H. Thus if all x have complexity K(x) >k, D carries >i bits of information on each its x where i+j ~ k. Note that there are no ways to generate D with significant I(D:H).
Keywords
Cite
@article{arxiv.1107.1458,
title = {Sets Have Simple Members},
author = {Samuel Epstein and Leonid A. Levin},
journal= {arXiv preprint arXiv:1107.1458},
year = {2014}
}
Comments
This paper has been withdrawn by the authors. Withdrawn (v8) by S. Epstein. Reposted as arXiv:1403.4539 by the coauthor