TY - GEN

T1 - Relative randomness for Martin-Löf random sets

AU - Peng, Ning Ning

AU - Higuchi, Kojiro

AU - Yamazaki, Takeshi

AU - Tanaka, Kazuyuki

PY - 2012

Y1 - 2012

N2 - Let Γ be a set of functions on the natural numbers. We introduce a new randomness notion called semi Γ-randomness, which is associated with a Γ-indexed test. Fix a computable sequence {G n} nεω of all c.e. open sets. For any f ε Γ, {G f(n)} nεω is called a Γ-indexed test if μ(G f(n)) ≤ 2 -n for all n. We prove that weak n-randomness is strictly stronger than semi Δ n 0-randomness, for n > 2. Moreover, we investigate the relationships between various definitions of randomness.

AB - Let Γ be a set of functions on the natural numbers. We introduce a new randomness notion called semi Γ-randomness, which is associated with a Γ-indexed test. Fix a computable sequence {G n} nεω of all c.e. open sets. For any f ε Γ, {G f(n)} nεω is called a Γ-indexed test if μ(G f(n)) ≤ 2 -n for all n. We prove that weak n-randomness is strictly stronger than semi Δ n 0-randomness, for n > 2. Moreover, we investigate the relationships between various definitions of randomness.

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U2 - 10.1007/978-3-642-30870-3_58

DO - 10.1007/978-3-642-30870-3_58

M3 - Conference contribution

AN - SCOPUS:84862157760

SN - 9783642308697

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 581

EP - 588

BT - How the World Computes - Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012, Proceedings

T2 - Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012

Y2 - 18 June 2012 through 23 June 2012

ER -