Cooperating array grammar systems

The aim of this paper is to elaborate the power of cooperation in generating pictures by array grammars. As it is expected, the generative capacity of cooperating array grammar systems (with a fixed number, with a number greater than a given threshold, or with the maximal number of derivation steps in each component when it is enabled) is strictly greater than that of context-free array grammars. Yet the same result is also obtained in the case of systems with regular components, which contradicts the corresponding result for string grammar systems. In fact, some more results for array grammar systems are obtained which either contradict the results for the corresponding string grammar systems or are not even known for these string grammar systems. Various non-context-free sets of arrays which can be generated in a simple way by cooperating array grammar systems are presented and show the power of the mechanism of cooperation for picture description.