ICGT 2006: Graph Transformations pp 122-137

# Matrix Approach to Graph Transformation: Matching and Sequences

• Pedro Pablo Pérez Velasco
• Juan de Lara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4178)

## Abstract

In this work we present our approach to (simple di-)graph transformation based on an algebra of boolean matrices. Rules are represented as boolean matrices for nodes and edges and derivations can be efficiently characterized with boolean operations only. Our objective is to analyze properties inherent to rules themselves (without considering an initial graph), so this information can be calculated at specification time. We present basic results concerning well-formedness of rules and derivations (compatibility), as well as concatenation of rules, the conditions under which they are applicable (coherence) and permutations. We introduce the match, which permits the identification of a grammar rule left hand side inside a graph. We follow a similar approach to the single pushout approach (SPO), where dangling edges are deleted, but we first adapt the rule in order to take into account any deleted edge. To this end, a notation borrowed from functional analysis is used. We study the conditions under which the calculated data at specification time can be used when the match is considered.

## Keywords

Graph Transformation Outgoing Edge Matrix Approach Graph Grammar Grammar Rule

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## Copyright information

© Springer-Verlag Berlin Heidelberg 2006

## Authors and Affiliations

• Pedro Pablo Pérez Velasco
• 1
• Juan de Lara
• 1
1. 1.Escuela Politécnica SuperiorUniversidad Autónoma de Madrid