Rule-level verification of graph transformations for invariants based on edges' transitive closure

Christian Percebois (1) , Martin Strecker (2) , Hanh Nhi Tran (1)

1 IRIT-MACAO - Modèles, Architectures, Composants, Agilité et prOcessus
2 IRIT-ACADIE - Assistance à la Certification d’Applications DIstribuées et Embarquées

This paper develops methods to reason about graph transformation rules for proving the preservation of structural properties, especially global properties on reachability. We characterize a graph transformation rule with an applicability condition specifying the matching conditions of the rule on a host graph as well as the properties to be preserved during the transformation. Our previous work has demonstrated the possibility to reason about a graph transformation at rulelevel with applicability conditions restricted to Boolean combinations of edge expressions. We now extend the approach to handle the applicability conditions containing transitive closure of edges, which implicitly refer to an unbounded number of nodes. We show how these can be internalized into a finite pattern graph in order to enable verification of global properties on paths instead of local properties on edges only.

Mots clés: Global property; Verification; Graph transformations; Formal methods; Transitive closure

Domaines: Génie logiciel [cs.SE]; Systèmes embarqués; Cryptographie et sécurité [cs.CR]; Interface homme-machine [cs.HC]; Architectures Matérielles [cs.AR]; Modélisation et simulation

Christian Percebois, Martin Strecker, Hanh Nhi Tran. Rule-level verification of graph transformations for invariants based on edges' transitive closure. 11th International Conference Software Engineering and Formal Methods (SEFM 2013), Sep 2013, Madrid, Spain. pp. 106-121. ⟨hal-01178554⟩