Computability and Randomness

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...

Randomness and Computability

This thesis establishes significant new results in the area of algorithmic randomness. These results elucidate the deep relationship between randomness and computability. A number of results focus on randomness for finite strings. Levin introduced two functions which measure the randomness of finite strings. One function is derived from a universal monotone machine and the other function is der...