On the Size of Components of Probabilistic Cooperating Distributed Grammar Systems

Abstract

Probabilistic cooperating distributed grammar systems introduced in [1] are systems of probabilistic grammars in the sense of [9], i.e., a probability is associated with any transition from one rule to another rule and with any transition from one probabilistic grammar to another probabilistic grammar; a probabilistic grammar 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 cut-point). 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 are 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 ET0L systems.

This research was supported in part under grant no. D-35/2000 and HUN009/00 by the Intergovernmental S&T Cooperation Programme of the Office of Research and Development Division of the Hungarian Ministry of Education and its German partner, the Federal Ministry of Education and Research (BMBF).