Efficient configuration and verification of software product lines
Proceedings of the 15th International Software Product Line Conference, Volume 2
Reducing multiplicities in class diagrams
Proceedings of the 14th international conference on Model driven engineering languages and systems
Configuration repair via flow networks
ISMIS'12 Proceedings of the 20th international conference on Foundations of Intelligent Systems
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The Unified Modeling Language (UML) has become a universal tool for the formal object-oriented specification of hard- and software. In particular, UML class diagrams and so-called multiplicities, which restrict the number of links between objects, are essential when using UML for applications like the specification of admissible configurations of components. In this paper we give a formal definition of the semantics of UML class diagrams and multiplicities. We extend results obtained in the context of Entity Relationship diagrams to cover UML specific extensions like the (non-)uniqueness attribute of binary associations. We show that the consistency of such specifications can be checked in polynomial time, and give an algorithm for computing minimal configurations (models). The core of our approach is a translation of UML class diagrams to Diophantine inequations.