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.

Graph transformation systems (GTSs) can be seen as well-structured transition systems (WSTSs) and via well-structuredness it is possible to obtain decidability results for certain classes of GTSs. We present a generic framework, parameterized over the well-quasi-order (wqo), in which several types of GTSs can be seen as (restricted) WSTSs. We instantiate this framework with three orders: the minor ordering, the subgraph ordering and the induced subgraph ordering. Furthermore we consider two case studies where we apply the theory to analyze a leader election protocol and a simple access rights management system with our tool Uncover.

Given a transition system and a partial order on its states, the coverability problem is the question to decide whether a state can be reached that is larger than some given state. For graphs, a typical such partial order is the minor ordering, which allows to specify "bad graphs" as those graphs having a given graph as a minor. Well-structuredness of the transition system enables a finite representation of upward-closed sets and gives rise to a backward search algorithm for deciding coverability. It is known that graph tranformation systems without negative application conditions form well-structured transition systems (WSTS) if the minor ordering is used and certain condition on the rules are satisfied. We study graph transformation systems with negative application conditions and show under which conditions they are well-structured and are hence amenable to a backwards search decision procedure for checking coverability.

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We introduce a new class of graph transformation systems in which rewrite rules can be guarded by universally quantified conditions on the neighbourhood of nodes. These conditions are defined via special graph patterns which may be transformed by the rule as well. For the new class for graph rewrite rules, we provide a symbolic procedure working on minimal representations of upward closed sets of configurations. We prove correctness and effectiveness of the procedure by a categorical presentation of rewrite rules as well as the involved order, and using results for well-structured transition systems. We apply the resulting procedure to the analysis of the Distributed Dining Philosophers protocol on an arbitrary network structure.