Random context structure grammars and automata-a formal approach

In an earlier paper, results of a research project to define grammars and automata of two and three dimensions were reported. In that paper, many of the relevant theorems were only discussed in a cursory way, and were not formally proved. In this paper we formalize the major concepts introduced. Because of current interest and the fact that the two-dimensional grammars and automata defined are but a special case of the three-dimensional grammars and automata, we concentrate on three-dimensional concepts. A brief overview of current three-dimensional grammars and automata is given. Formal definitions for random context structure grammars and random context structure automata are given. A formal proof is given for the equivalence of the class of languages generated by random context structure grammars and the class of languages accepted by random context structure grammars.