Simplification and Correctness of UML Class Diagrams - Focusing on Multiplicity and Aggregation/Composition Constraints

Model-driven Engineering requires efficient powerful methods for verifying model correctness and quality. Class Diagram is the central language within UML. Its main problems involve correctness problems, which include the consistency and the finite satisfiability problems, and quality problems, which include the redundancy and incomplete design problems. Two central constraints in class diagrams are the multiplicity and the aggregation/composition constraints. They are essential in modeling configuration management, features, biology, computer-aided design and database systems. The contribution of this paper involves efficient algorithms for tightening multiplicity constraints that cannot be realized, and for identification of correctness problems that are caused by aggregation/composition constraints. The algorithms are analyzed, and their soundness and completeness properties are proved. We show that these constraints are inter-related, and that the combination of these algorithms strengthens their results.