General CD Grammar Systems and Their Simplification

general grammars, CD grammar systems, simulated non-context-free rules, homogeneous rules, evenly homogeneous rules

The present paper studies general CD grammar systems, whose components are general grammars, so they are computationally complete, and it investigates them working under the * mode and t mode. Most importantly, the paper presents two types of transformations that turn arbitrary general grammars into equivalent two-component general CD grammar systems with a context-free component and a non-context-free component. From the first type of transformations, the non-context-free component results with two rules of the form 11->00 and 0000->epsilon, while the other type of transformations produces the non-context-free component with two rules of the form 11->00 and 0000->2222. Apart from this significant reduction and simplification, the paper describes several other useful properties concerning these systems and the way they work. A formulation of several remarks and open problems closes this paper.