A General Framework for Well-Structured Graph Transformation Systems

TL;DR

This paper introduces a comprehensive framework that unifies various graph transformation systems under well-structured transition systems, enabling decidability analysis through specific orderings like subgraph and induced subgraph orderings.

Contribution

It extends previous work by generalizing the well-structuredness approach to multiple graph orderings within a unified framework.

Findings

Framework successfully models different GTSs as WSTSs

Application to access rights management system demonstrates practical utility

Subgraph and induced subgraph orderings facilitate analysis

Abstract

Graph transformation systems (GTSs) can be seen as wellstructured transition systems (WSTSs), thus obtaining decidability results for certain classes of GTSs. In earlier work it was shown that wellstructuredness can be obtained using the minor ordering as a well-quasiorder. In this paper we extend this idea to obtain a general framework in which several types of GTSs can be seen as (restricted) WSTSs. We instantiate this framework with the subgraph ordering and the induced subgraph ordering and apply it to analyse a simple access rights management system.