Deriving Bisimulation Congruences in the Presence of Negative Application Conditions

In recent years there have been several approaches for the automatic derivation of labels from an unlabeled reactive system. This can be done in such a way that the resulting bisimilarity is automatically a congruence. One important aspect that has not been studied so far is the treatment of reduction rules with negative application conditions. That is, a rule may only be applied if certain patterns are absent in the vicinity of a left-hand side. Our goal in this paper is to extend the borrowed context framework to label derivation with negative application conditions and to show that bisimilarity remains a congruence. An important application area is graph transformation and we will present an example in terms of blade server systems in order to illustrate the theory.