Occam Bound on Lowest Complexity of Elements
Computational Complexity
2018-12-03 v2
Abstract
The combined universal probability M(D) of strings x in sets D is close to max_{x \in D} M({x}): 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 x where i+j ~ k. Note, there are no ways (whether natural or artificial) to generate D with significant I(D:H).
Cite
@article{arxiv.1403.4539,
title = {Occam Bound on Lowest Complexity of Elements},
author = {Leonid A. Levin},
journal= {arXiv preprint arXiv:1403.4539},
year = {2018}
}
Comments
4 pages, minor clarifications