Matrix Graph Grammars

Perez Velasco, Pedro Pablo (2008) Matrix Graph Grammars. PhD thesis, Computer Science, Computer Science Department.

Abstract

If the aim of this dissertation had to be summarized in a single sentence, it could be algebraization of graph grammars. An equivalent one would be study of graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely algebraic approach does not exist up to now. A Chomsky (or string) grammar is, roughly speaking, a precise description of a formal language (which in essence is a set of strings). On a more discrete mathematical style, it can be said that graph grammars – Matrix Graph Grammars in particular – study dynamics of graphs. Ideally, this algebraization would enforce our understanding of grammars in general, providing new analysis techniques and generalizations of concepts, problems and results known so far. In this dissertation we fully develop such theory over the field GF(2) which covers all graph cases, from simple graphs (more attractive for a mathematician) to multidigraphs (more interesting for an applied computer scientist). The theory is presented and its basic properties demonstrated in a first stage, moving to increasingly difficult problems and establishing relations among them.