Sets Have Simple Members

Details Sets Have Simple Members Sets Have Simple Members

2011-07-07

arxiv.org/abs/1107.1458v5

Computer Science

Computational Complexity

3 pages, minor simplifications

Scientific paper

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).

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