Cooperating Distributed Grammar Systems with Permitting Grammars as Components

This paper studies cooperating distributed grammar systems working in the terminal derivation mode where the components are variants of permitting grammars. It proves that although the family of permitting languages is strictly included in the family of random context languages, the families of random context languages and languages generated by permitting cooperating distributed grammar systems in the above mentioned derivation mode coincide. Moreover, if the components are so-called left-permitting grammars, then cooperating distributed grammar systems in the terminal mode characterize the class of context-sensitive languages, or if erasing rules are allowed, the class of recursively enumerable languages. Descriptional complexity results are also presented. It is shown that the number of permitting components can be bounded, in the case of left-permitting components with erasing rules even together with the number of nonterminals.