Cooperating Distributed Grammar Systems with Random Context Grammars as Components

Abstract

In this paper, we discuss cooperating distributed grammar systems where components are (variants of) random context grammars. We give an overview of known results and open problems, and prove some further results.

Left-forbidding cooperating distributed grammar systems

“…(X → ε, ∅), for all X ∈ {A, B, C , D}, (7) ($ → ε, {A, B, C , D, A , B , C , D , S , S}), and P 2 contains these productions: (9) (C → C , {A, C , A , C }), (10) (B → B , {B, D, B , D }), (11) (D → D , {B, D, B , D }), (12) ($ → $, {B , C }), (13) …”

“…In view of these results, the results of the present paper are of some interest because the cooperation increases the generative power of cooperating distributed grammar systems with left-forbidding components from the power of context-free grammars to the power of context sensitive or phrase structure grammars. On the other hand, however, this increase does not hold for cooperating distributed grammar systems with random context components because they are as powerful as random context grammars (see [9,10]). Consequently, although random context grammars are more powerful than left-forbidding grammars, cooperating random context grammars are not as powerful as cooperating left-forbidding grammars.…”