Finite-state probabilistic languages

For semi-Thue systems the notion of probabilistic rule is introduced. Based on probabilistic rules, probabilistic grammars and languages generated by these grammars with a standard probabilistic characteristic relation are defined. Our probabilistic grammars differ from those proposed by Salomaa (1969).It is shown that a language can be represented in a finite probabilistic automaton iff it is a finite-state probabilistic unambiguous language; the family of finite-state probabilistic languages (of type 3) on a given alphabet forms a Boolean algebra; the family of context-free probabilistic languages is identical with the family of finite-state probabilistic languages