A relatively longstanding question in algorithmic randomness is Jan Reimann's question whether there is a Turing cone of broken dimension. That is, is there a real A such that...
Consider the problem of calculating the fractal dimension of a set X consisting of all infinite sequences S over a finite alphabet that satisfy some given condition P on the asympt...
Following Lutz’s approach to effective (constructive) dimension, we define a notion of dimension for individual sequences based on Schnorr’s concept(s) of randomness. In contr...