Graph and model transformations play a central role for visual modeling and model-driven software development. Within the last decade, a mathematical theory of algebraic graph and model transformations has been developed for modeling, analysis, and to show the correctness of transformations. Ulrike Golas extends this theory for more sophisticated applications like the specification of syntax, semantics, and model transformations of complex models. Based on M-adhesive transformation systems, model transformations are successfully analyzed regarding syntactical correctness, completeness, functional behavior, and semantical simulation and correctness. The developed methods and results are applied to the non-trivial problem of the specification of syntax and operational semantics for UML statecharts and a model transformation from statecharts to Petri nets preserving the semantics.

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