Occam Bound on Lowest Complexity of Elements
arXiv:1403.4539 · doi:10.1016/j.apal.2014.01.006
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).
4 pages, minor clarifications