On the Descriptional Complexity of External Hybrid Cooperating Distributed Grammar Systems

In this paper we investigate descriptional complexity aspects of external hybrid cooperating distributed (CD) grammar systems. An external hybrid CD grammar system consists of several grammars called components. The cooperation between the components is controlled by the derivation mode that determines when a component becomes active or inactive. We set our focus on the number of components and the maximum number of productions in a component. For some external hybrid CD grammar systems it is possible to find equivalent systems that consist of only five components. For these external hybrid CD grammar systems we can also construct equivalent systems with at most six productions in a component. If one of the two parameters is fixed, the other one induces an infinite hierarchy of language classes.