By Ulrike Golas

Graph and version adjustments play a primary function for visible modeling and model-driven software program improvement. in the final decade, a mathematical thought of algebraic graph and version modifications has been constructed for modeling, research, and to teach the correctness of variations. Ulrike Golas extends this thought for extra refined purposes just like the specification of syntax, semantics, and version changes of advanced versions. in accordance with M-adhesive transformation structures, version ameliorations are effectively analyzed concerning syntactical correctness, completeness, sensible habit, and semantical simulation and correctness. The built tools and effects are utilized to the non-trivial challenge of the specification of syntax and operational semantics for UML statecharts and a version transformation from statecharts to Petri nets holding the semantics.

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**Example text**

These forward and backward transformations can be deduced automatically, requiring only one description for both directions. This eases the speciﬁcation of bidirectional model transformations. In [KS06] it is shown how to split a triple rule tr into a source rule trS , describing the changes in the source graph, and a forward rule trF , describing the corresponding update of the target graph. It follows that also transformations can be split up into a source and forward transformation. As a result, the forward rules specify the actual forward model transformation.

It might be expected that, at least in the category Sets, every pushout is a van Kampen square. Unfortunately, this is not true, but at least pushouts along monomorphisms are van Kampen squares in Sets and several other categories. For an M-adhesive category, we consider a category C together with a morphism class M of monomorphisms. We require pushouts along Mmorphisms to be M-van Kampen squares, along with some rather technical conditions for the morphism class M which are needed to ensure compatibility of M with pushouts and pullbacks.

Amalgamation [Tae96] is used for the parallel execution of synchronized rules. We can model an arbitrary number of parallel actions, which are somehow linked, at diﬀerent places in a model, where the number of actions is not known beforehand. To model this situation with standard graph transformation, we had to apply the rules sequentially with an explicitly coded iteration, but this is neither natural nor eﬃcient and often complicated. For example, for the ﬁring semantics of Petri nets, with amalgamation we only need one rule where we can collect all pre- and post-places and execute the complete ﬁring step.