On the notion of a probabilistic algorithm.

Abstract

An earlier paper gives an account of a quest for a satisfactory formalization of the classical informal notion of an algorithm. In this paper, an attempt is made to generalize the results of that quest to the notion of a probabilistic algorithm, i.e. an algorithm that expresses a pattern of behaviour in which probabilistic choices occur. The central notions in this paper are the notion of a probabilistic proto-algorithm and the notion of algorithmic equivalence of probabilistic proto-algorithms. Probabilistic algorithms are considered to be equivalence classes of probabilistic proto-algorithms under algorithmic equivalence. This means that the notion of a probabilistic algorithm is explained without using any particular machine model or algorithmic language.