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This article proposes a method for proving the correctness of graph algorithms by manipulating their spanning trees enriched with additional references. We illustrate this concept with a proof of the correctness of a (pseudo-)imperative version of the Schorr-Waite algorithm by refinement of a functional one working on trees. It is composed of two orthogonal steps of refinement-functional to imperative and tree to graph-finally merged to obtain the result. Our imperative specifications use monadic constructs and syntax sugar, making them close to common imperative languages. This work has been realized within the Isabelle/HOL proof assistant.

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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.

The correctness of transformations has recently begun to attract the attention of the researchers in Model Driven Engineering (MDE). The objective of this article is twofold. First, it presents an approach for transforming BPMN models to Colored Petri nets models using GROOVE and EMF/Xpand tools. Second, it proposes an approach for checking the correctness of the transformation itself. More precisely, we have defined the termination property of the transformation and the preservation of some structural properties of BPMN models by the transformation using the GROOVE graph transformation tool. The authors have also applied the approach on a case study through which the authors have verified the successful termination of the transformation using GROOVE Model Checker and the target model properties using CPN Tools.