Random Context in Regulated Rewriting Versus Cooperating Distributed Grammar Systems

It is well known that certain language families generated by cooperating distributed (CD) grammar systems can be characterized in terms of context-free random context grammars. In particular, the language families generated by CD grammar systems working in the t- and sf-modes of derivation obey a characterization in terms of ETOL systems, or equivalently by context-free disjoint forbidding random context grammars, and of context-free random context grammars with appearance checking, respectively. Now the question arises whether or not other random context like language families can be characterized in terms of CD grammar systems. We positively answer this question, proving that there are derivation modes for CD grammar systems, namely the negated versions of the aforementioned modes, which precisely characterize the family of context-free disjoint forbidding random context languages and that of languages generated by context-free random context grammars without appearance checking. In passing we show that every language generated by a context-free random context grammar without appearance checking can also be generated by a context-free recurrent programmed grammar without appearance checking, and vice versa.