Comparing notions of randomness

Abstract. It is an open problem in the area of effective (algorithmic) randomness whether Kolmogorov-Loveland randomness coincides with Martin-L¨of randomness. Joe Miller and Andr´e 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-L¨of randomness. Since in its proof some of the ideas we use are clearer, we also show the weaker theorem that permutation randomness is weaker than Martin-L¨of randomness.

• Type: Journal
• Year: 2010
• Where: TCS
• Authors: Bart Kastermans, Steffen Lempp
• Keywords: Kolmogorov-Loveland Randomness, Martin-L¨of Randomness, Randomness, TCS 2010, Theoretical Computer Science