Nested graph transformation units

In this paper, we introduce a new concept for the structured development of rule-based graph transformation systems that allows to build up large systems from small pieces in a modular way. The concept is called nested graph transformation unit and consists of a network of local graph transformation units. While each local unit provides a set of rules and control conditions (including input and output descriptions), the net reflects the import structure of the system where each local unit can use its direct neighbours without any restrictions. In particular, the import structure may contain cycles. It is shown that nested graph transformation units have a reasonable operational semantics by iterating the so-called interleaving operator, which interleaves local rule applications with calls of used units according to the local control conditions. It turns out that the iterated interleaving semantics is the smallest fixed point of the interleaving operator provided that the involved control conditions are continuous in a certain sense.