This paper discusses the basic properties of the probabilistic push-down automaton (PPDA). Intuitively speaking, PPDA is obtained by adding a probabilistic property to the nondeterministic transition of the nondeterministic push-down automaton (NPDA). According to the property of the error in the accepting condition, PPDA is classified into a two-sided error PPDA, a one-sided error PPDA, and bounded error PPDA. Moreover, the acception error is considered not only for 1/2, but also for an arbitrary cut-point, to discuss the relations among classes of languages. Major results are as follows.



The class of languages accepted by bounded error PPDA is not the same as that accepted by NPDA. In the case of two-sided error PPDA and the bounded error PPDA, the class of acceptable languages does not depend on the cut-point. In the case of a one-sided PPDA, the class of acceptable languages depends to some extent on the cut-point. In other words, there exists an infinite hierarchy. Kolmogorov complexity is used in the proof of the major theorem.

Probabilistic automata push-down

A note on noncontext-free rational stochastic languages

It is known that nonregular languages can be accepted by finite state probabilistic automata. For many years it was not known whether a finite state probabilistic automaton existed that would accept a context sensitive language that is not context free. Such a finite state probabilistic automaton is constructed.

Kuo An Chen

Papers

A finite state probabilistic automaton that accepts a context sensitive language that is not context free