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Abstract. The aim of the paper is to introduce the notion of a transformation unit together with its interleaving semantics and to study it as a means of constructing large graph transformation systems from small ones in a structured and systematic way. A transformation unit comprises a set of rules, descriptions of initial and terminal graphs, and a control condition. Moreover, it may import other transformation units for structuring purposes. Its semantics is a binary relation between initial and terminal graphs which is given by interleaving sequences. As a generalization of ordinary derivations, an interleaving sequence consists of direct derivation steps interleaved with calls of imported transformation units. It must obey the control condition and may be seen as a kind of structured derivation. The introduced framework is independent of a particular graph transformation approach and, therefore, it may enhance the usefulness of graph transformations in many contexts.

Abstract. This paper studies the semantics of a central part of the Unified Modeling Language UML. It discusses UML class, object and state diagrams and presents a new integrated semantics for both on the basis of graph transformation. Graph transformation is a formal technique having some common ideas with the UML. Graph transformation rules are associated with the operations in class diagrams and with the transitions in state diagrams. The resulting graph transformations are combined into a one system in order to obtain a single coherent semantic description.

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.