Computability, Complexity and Randomness

Computability, Algorithmic Randomness and Complexity

I think mathematical ability manifests itself in many different ways. In particular, mathematicians can be drawn to space and geometry, can have strong analytic intuition, can be drawn to formalism, they can be drawn to counting arguments, etc. There is definitely no unique type of mathematician. Maybe those mathematicians who are drawn to algorithmic thinking have found a home in computer scie...

Algorithmic Randomness and Computability

We examine some recent work which has made significant progress in out understanding of algorithmic randomness, relative algorithmic randomness and their relationship with algorithmic computability and relative algorithmic computability. Mathematics Subject Classification Primary 68Q30, 68Q15, 03D15, 03D25, 03D28, 03D30.

Randomness, Computability, and Density

We study effectively given positive reals (more specifically, computably enumerable reals) under a measure of relative randomness introduced by Solovay [32] and studied by Calude, Hertling, Khoussainov, and Wang [6], Calude [2], Kučera and Slaman [20], and Downey, Hirschfeldt, and LaForte [15], among others. This measure is called domination or Solovay reducibility, and is defined by saying tha...

Computability and randomness

Randomness, Computability and Information

Question 1: Why were you initially drawn to the study of computation and randomness? It is easy to go back and find the signposts that seem to point to the present. By only telling the right parts of my story, I can make it sound like I was destined to become a computability theorist studying randomness. The truth is that the outcome was never clear to me, but there are certainly signposts wort...