Comparing notions of randomness

Authors:
Bart Kastermans;Steffen Lempp
Affiliations:
Department of Mathematics, University of Colorado, Boulder, CO 80309, United States;Department of Mathematics, University of Wisconsin, Madison, WI 53706-1388, United States
Venue:
Theoretical Computer Science
Year:
2010

Citing 6
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Abstract

It is an open problem in the area of effective (algorithmic) randomness whether Kolmogorov-Loveland randomness coincides with Martin-Lof randomness. Joe Miller and Andre Nies suggested some variations of Kolmogorov-Loveland randomness to approach this problem and to provide a partial solution. We show that their proposed notion of injective randomness is still weaker than Martin-Lof randomness. Since in this proof some of the ideas we use are clearer, we also show the weaker theorem that permutation randomness is weaker than Martin-Lof randomness.