# Removing redundant multiplicity constraints in UML class models

## Abstract

Models are central for the development and management of complex systems. In order to be useful along the entire life cycle of software they must provide reliable support and enable automatic management. For that purpose, they must be precise, consistent, correct, and be subject to stringent quality verification and control criteria. Model automation calls for deep formal study of models, so that tools can provide inclusive support to users. This paper deals with optimization of multiplicity constraints in *Class Models*, i.e., models that provide abstraction on the static structure of software. The paper introduces an in-depth analysis of *redundancy* of multiplicity constraints, i.e., multiplicities that cannot be realized in any legal instance. The analysis includes: (1) a formal study of gaps of redundancies in multiplicity intervals; (2) algorithmic and rule-based methods for removing redundancies in multiplicity constraints; (3) a formal study of completeness of the algorithmic procedures, with respect to most UML class model constraints. The algorithmic procedures are implemented in our * FiniteSatUSE* tool. To the best of our knowledge, there is no previous study of properties of multiplicity redundancy, no completeness analysis of tightening methods, and no systematic study of these features with respect to most UML class model constraints.

## Keywords

Class models MBSE Formal semantics Multiplicity constraints Correctness Quality Redundancy Verification Boundary tight Tightening methods Model optimization Multiplicity tightening Tightening rules## References

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