Equivalent characterizations of partial randomness for a recursively enumerable real

Details Equivalent characterizations of partial randomness for a recursively enumerable real Equivalent characterizations of partial randomness for a recursively enumerable real

2008-05-17

arxiv.org/abs/0805.2691v1

Computer Science

Information Theory

19 pages, LaTeX2e, no figures

Scientific paper

A real number \alpha is called recursively enumerable if there exists a computable, increasing sequence of rational numbers which converges to \alpha. The randomness of a recursively enumerable real \alpha can be characterized in various ways using each of the notions; program-size complexity, Martin-L\"{o}f test, Chaitin's \Omega number, the domination and \Omega-likeness of \alpha, the universality of a computable, increasing sequence of rational numbers which converges to \alpha, and universal probability. In this paper, we generalize these characterizations of randomness over the notion of partial randomness by parameterizing each of the notions above by a real number T\in(0,1]. We thus present several equivalent characterizations of partial randomness for a recursively enumerable real number.

Affiliated with

Also associated with

No associations

Rating

Equivalent characterizations of partial randomness for a recursively enumerable real does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Equivalent characterizations of partial randomness for a recursively enumerable real, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equivalent characterizations of partial randomness for a recursively enumerable real will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-614693