Pullback rewriting and applications
Michel Bauderon, Hélène Jacquet, Renate Klempien-Hinrichs · Electronic Notes in Theoretical Computer Science · 2002
Following the tradition of language theory, the majority of the approaches to graph rewriting, be they presented in a categorical, algebraic, or set-theoretic framework, relied upon a notion of substitution consisting of union followed by identification. Trying to devise a categorical framework for node rewriting showed that another approach was possible, using product rather than union and inclusion rather than identification. This dual approach led to the development of pullback rewriting, whose applications seem very promising. In this paper, we review the basic definitions and results of the pullback approach of graph rewriting which were developed during the EU TMR Project GETGRATS.