On the Generative Power of CD Grammar Systems With Scattered Context Components

There is a long time open problem regarding the generative power of scattered context grammars without erasing rules. This problem tries to compare their generative power with context-sensitive grammars. In this paper, modified version of this problem will be presented. This modified version combines scattered context grammars with another model — grammar systems. It will be shown that when considering this modified version of the problem, those two models have indeed same generative power. Furthermore, it will be shown that this property holds even for grammar systems with only two components where each component contains only scattered context rules with degree of two or less. Even though this does not solve the original problem, this modified version can be useful when solving the standard variant of the problem.