Similarities Between String Grammars and Graph Grammars

In this paper, we present some studies about relations existing between well known Chomsky string grammars and graph grammars, in particularly hypergraph grammars. We are discussing about deterministic context free Lindenmayer Systems used to describe commands to a device that generates black and white digital images. Instead of well-known methods of drawing, we will paint squares, not lines. After that, we give some important properties of growth functions of D0L-systems. In addition, we turn the discussion to gray scale or color digital image generation. The second main part of the paper is about normal forms of hyperedge replacement grammars. In context freeness of these grammars, we can transform each of it into an equivalent grammar without λ-productions and without rewritings. After that, in a nondeterministic way, we will create equivalent grammars in Chomsky Normal Form or Greibach Normal Form. Both normal forms are inspired by string grammars. In the third part of this paper we illustrate some important differences between graph grammars and hypergraph grammars in context of freeness. On the other hand, we give a possibility to transform the planar structure of a hypergraph into a linear one with concern of determinism. This can create a path to transform a pushdown automaton into a generative grammar equivalent. Keywords—Chomsky, Context Freeness, Deterministic, Deterministic Context Free Lindenmayer Systems (D0L-systems), Digital Pictures, Graph Grammars, Greibach, Growth Functions, Hyperedge Replacement Grammars, Nondeterministic, Nondeterministic, Normal Form, Turtle.