On Competence in CD Grammar Systems

We investigate the generative power of cooperating distributed grammar systems (CDGSs), if the cooperation protocol is based on the level of competence on the underlying sentential form. A component is said to be =k-competent (≤k-, ≥k-competent, resp.) on a sentential form if it is able to rewrite exactly k (at most k, at least k, resp.) different nonterminals appearing in that string. In most cases CDGSs working according to the above described cooperation strategy turn out to give new characterizations of the language families based on random context conditions, namely random context (context-free) languages and the biologically motivated family of languages generated by ET0L systems with random context. Thus, the results presented in this paper can shed new light on some longstanding open problems in the theory of regulated rewriting.