Context-Free Graph Grammars

Graph grammars have been studied by several authors. The motivations of these works have arisen from completely different areas of computer science, such as picture processing (Pfaltz and Rosenfeld, 1969; Montanari, 1970; Rosenfeld and Milgram, 1972; Pavlidis, 1972; Abe et al., 1973; Furtado and Mylopoulos, 1975; Fu and Brayer, 1975) or formal semantics of programming languages (Pratt, 1971). In particular, our interest derives from studies in data structure definition, abstraction, and correctness (Della Vigna and Ghezzi, 1976). The large variety of motivations seems to be responsible for the unnormalized notations which have been introduced. Almost every author set his own definitions, so that properties and theorems cannot be readily transferred from one formal model to another. Context-free graph grammars have been defined by Pavlidis (1972) and Pratt (1971); in particular, we will base our work on the model described by Pratt. In this paper context-free graph grammars are studied in order to develop a theory similar to that of context-free string languages. In particular, some results are shown on the generative power of the scheme, the existence of normal forms, and the parsing problem.