R70-3 On Stochastic Languages

A stochastic language is a set of words accepted by a probabilistic automaton with some cutpoint. The structure of the family of stochastic languages may not parallel the structure of the family of regular languages. Some stochastic languages are context-free languages which are nonregular. The basic questions of when the complement of a stochastic language is a stochastic language, or when the intersection or union of two stochastic languages is stochastic, have not been solved but have been illuminated by Turakainen´s work. Turakainen proves that like the context-free languages, the intersection of a stochastic language and a regular language is a stochastic language. He shows as well that the union of a stochastic language and regular language is also a stochastic language. All right derivatives of a stochastic language are stochastic languages. In the same volume as Turakainen´s paper, Nasu and Honda have proven what amounts to the fact that the reversal of a stochastic language is a stochastic language. They also show other basic properties.