A Note on the Cooperation in Rewriting Systems with Context-Dependency Checking

Extended Abstract Rewriting systems based on simple forms of productions play an important role in formal language theory. Therefore, it is no surprise that context-free grammars and their modifications are one of the most studied models. However, many of the systems describing practically interesting applications, such as the parsers of natural and programming languages, require additional mechanisms that allow these systems to check for some kind of context dependencies. From that point of view, context-free grammars are not convenient for those applications because they are too simple to describe such context dependencies. Naturally, a method how to increase the generative power of rewriting systems is to compose them of several simple components, and to define how these components cooperate to generate the common sentential form. In the literature , such devices are called cooperating distributed (CD) grammar systems. Specifically, CD grammar systems [1] are rewriting devices composed of several components represented by grammars or other rewriting systems, and of a protocol describing the mutual cooperation of components in the generative process. These protocols describe (roughly speaking) the number of steps the component has to make to allow another component to work. For instance, the most interesting protocol is so-called terminal mode making the component work until it is not able to make another derivation step. It is well-known that the cooperation (as specified above) has a significant effect on context-free grammars—nontrivial cooperation protocols make context-free CD grammar systems more powerful than context-free grammars (the reader is referred to [2]). As mentioned above, simple rewriting devices that are able to check for some context dependencies are of interest. One of such simple rewriting systems, so-called random context grammars (see [3]), is a natural generalization of context-free grammars, where a mechanism checking for context dependencies is added. Specifically, two finite sets of nonterminal symbols are attached to each context-free production—a permitting and a forbidding set—and such a production is applicable only if all permitting symbols appear in the current sentential form, while no forbidding symbol does. It is known that the family of random context languages contains the whole family of context-free languages and that is properly included in the family of context sensitive languages. In addition, considering