By Ulrike Golas

ISBN-10: 3834814938

ISBN-13: 9783834814937

Graph and version variations play a principal position for visible modeling and model-driven software program improvement. in the final decade, a mathematical idea of algebraic graph and version differences has been built for modeling, research, and to teach the correctness of differences. Ulrike Golas extends this idea for extra subtle functions just like the specification of syntax, semantics, and version ameliorations of complicated versions. in line with M-adhesive transformation platforms, version changes are effectively analyzed relating to syntactical correctness, completeness, practical 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 conserving the semantics.

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**Additional info for Analysis and Correctness of Algebraic Graph and Model Transformations**

**Example text**

The compatibility with the opFi (dk ) Gi (d ) i i erations. For all i ∈ I we Fi (nk ) Gi (n ) opL i i i Fi (Lki ) Gi (L i ) have that Gi (m i ) ◦ opL i ◦ Fi (dki ) = opC Fi (mk ) Gi (m ) i ◦ Fi (mki ) ◦ i i Fi (dki ) = opC i ◦ Fi (nki ) = K Fi (Cki ) Gi (C i ) Gi (n i ) ◦ opi = Gi (m i ) ◦ opC i Gi (d i ) ◦ opK i , and since K Gi (m i ) is an isomorphism it follows that opL i ◦ Fi (dki ) = Gi (d i ) ◦ opi , i. e. d ∈ G. 2. This is obvious. 3. This follows directly from Item 1, since any comma category is an instantiation of a general comma categories.

But the knowledge of the domain-speciﬁc nature of the models may help to perform veriﬁcation with reasonable eﬀort. In [Erm09], a conceptual overview on model transformations based on graph transformations is given, especially regarding research activities and future work for the analysis and veriﬁcation of model transformations. For the veriﬁcation of model transformations, some results for syntactical correctness are available. Using the above mechanism, the correct typing of the target model is implied by the graph transformation approach.

Moreover, only a short outline of the theory of Madhesive transformation systems is given here. For the entire theory with all deﬁnitions, theorems, proofs, and examples see [EEPT06, EP06, PE07]. U. 1 Graphs, Typed Graphs, and Typed Attributed Graphs Graphs and graph-like structures are the main basis for (visual) models. Basically, a graph consists of nodes, also called vertices, and edges, which link two nodes. Here, we consider graphs which may have parallel edges as well as loops. A graph morphism then maps the nodes and edges of the domain graph to these of the codomain graph such that the source and target nodes of each edge are preserved by the mapping.

### Analysis and Correctness of Algebraic Graph and Model Transformations by Ulrike Golas

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