Undecidable Control Conditions in Graph Transformation Units

Graph transformation units are an approach-independent concept for programming by applying rules and imported transformation units to graphs, starting in an initial and ending in a terminal graph. This transformation process has to obey a so-called control condition, i.e. the device to select how rules or imported transformation units are to be combined in the transformation process executed by the unit. While the other parts of a unit may simply be required to be computable, this is too restrictive for control conditions. In this paper, we show that the semantics of certain control conditions is in general undecidable already when a single imported transformation unit occurs in the condition, and discuss the consequences for programming with graph transformation units.