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.