Graph grammars according to the type of input and manipulated data: A survey

Graph grammars which generate graphs are a generalization of Chomsky grammars that generate strings. During the last decades there has been a remarkable development of graph grammars. Due to their wide diversity of applications, graph grammars have received a particular attention from many scientists and researchers. There has been applications of graph grammars in several areas such as pattern recognition, data base systems, biological developments in organisms, semantics of programming languages, compiler construction, software development environments, etc. In the literature, in some surveys, graph grammars have been studied and classified according to some criteria such as: parallel or sequential applicability of rules, embedding mechanism, type of generated graphs, etc. In addition to this, as data play an important role more and more in different domains, we survey in this paper the vast field of graph grammars by classifying them according to three criteria: the number of manipulated data (single or multiple types), the nature of data (structured or unstructured), and finally the kind of data (images, graphs, patterns, etc.). In particular, we consider that a graph grammar is well defined by five components instead of four, namely: type of generated graphs (TG), a start graph (Z), a set of production rules (P), a set of additional specifications of the rules (A), and the criterion that we additionally consider which is the type of input and manipulated data (TD). This proposed formalism, especially with the added fifth component, may serve to overcome some issues related to Big Data and Cloud Computing domains.