The power of programmed grammars with graphs from various classes

Abstract

Programmed grammars, one of the most important and well investigated classes of grammars with context-free rules and a mechanism controlling the application of the rules, can be described by graphs. We investigate whether or not the restriction to special classes of graphs re- stricts the generative power of programmed grammars with erasing rules and without appearance checking, too. We obtain that Eulerian, Hamil- tonian, planar and bipartite graphs and regular graphs of degree at least three are pr-universal in that sense that any language which can be gener- ated by programmed grammars (with erasing rules and without appearance checking) can be obtained by programmed grammars where the underly- ing graph belongs to the given special class of graphs, whereas complete graphs, regular graphs of degree 2 and backbone graphs lead to proper subfamilies of the family of programmed languages.