76 citations · 76 across the 3 of their papers we have counts for
5 papers
Relativized depth
Laurent Bienvenu, Valentino Delle Rose, Wolfgang Merkle
Bennett's notion of depth is usually considered to describe the usefulness and internal organization of the information encoded into an object such as an infinite binary sequence.…
Normalized Information Distance and the Oscillation Hierarchy
Klaus Ambos-Spies, Wolfgang Merkle, Sebastiaan A. Terwijn
We study the complexity of approximations to the normalized information distance. We introduce a hierarchy of computable approximations by considering the number of oscillations. T…
Solovay functions and their applications in algorithmic randomness
Laurent Bienvenu, Rod Downey, Wolfgang Merkle +1
Classical versions of Kolmogorov complexity are incomputable. Nevertheless, in 1975 Solovay showed that there are computable functions such that for infinitely many st…
Separations of non-monotonic randomness notions
Laurent Bienvenu, Rupert Hoelzl, Thorsten Kraling +1
In the theory of algorithmic randomness, several notions of random sequence are defined via a game-theoretic approach, and the notions that received most attention are perhaps Mart…
Kolmogorov complexity and the Recursion Theorem
Bjørn Kjos-Hanssen, Wolfgang Merkle, Frank Stephan
Several classes of DNR functions are characterized in terms of Kolmogorov complexity. In particular, a set of natural numbers A can wtt-compute a DNR function iff there is a nontri…