Fairness, Computable Fairness and Randomness

Motivated by the observation that executions of a probabilistic system almost surely are fair, we interpret concepts of fairness for nondeterministic processes as partial descriptions of probabilistic behavior. We propose computable fairness as a very strong concept of fairness, attempting to capture all the qualitative properties of probabilistic behavior that we might reasonably expect to see in the behavior of a nondeterministic system. It is shown that computable fairness does describe probabilistic behavior by proving that runs of a probabilistic system almost surely are computable fair. We then turn to the question of how sharp an approximation of randomness is obtained by computable fairness by discussing completeness of computable fairness for certain classes of path properties