On the size of components of probabilistic cooperating distributed grammar systems

Probabilistic cooperating distributed grammar, systems introduced in [1] axe systems of probabilistic grammars in the sense of any transition from one rule to [9], i.e., a probability is associated wit another rule and with any transition from one probabilistic grammar to-another probabilistic grammar; a probabilistic grammer stops, if the chosen rule cannot be applied; and the generated language contains only words where the product of the transitions is larger than a certain cutpoint). We study the families obtained with cut-point 0 by restricting the number of rules in a probabilistic component. We show that at most two productions in any component axe sufficient to generate any recursively enumerable language. If one restricts to probabilistic components with one production in any component, then one obtains the family of deterministic ETOL systems.