PROBABILISTIC MACHINES AND LANGUAGES

Abstract

In the past several years, there has been an increasing interest in the study of probabilistic machines, grammars, and families of languages associated with these machines and/or grammars. However, until now, the emphasis has been placed on the study of the structures of the particular probabilistic machines, grammars, and/or families of languages. The main objective of the present paper is to develop a general treatment for probabilistic machines and languages. A formulation of an abstract model of probabilistic machines is presented. Various families of random languages associated with this model of probabilistic machines are studied and characterized. Since the model is general enough to encompass all existing types of probabilistic machines, the results obtained in this paper includes many of the known results as special cases. They also provide insights to the underlying structures of probabilistic machines and languages.