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Software and Systems Modeling
Erschienen in: Software and Systems Modeling 4/2019

14.09.2018 | Regular Paper

Removing redundant multiplicity constraints in UML class models

verfasst von: Mira Balaban, Azzam Maraee

Erschienen in: Software and Systems Modeling | Ausgabe 4/2019

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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.
Vorheriger Artikel DALEC: a framework for the systematic evaluation of data-centric approaches to process management software
Nächster Artikel Evaluating user interface generation approaches: model-based versus model-driven development

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Fußnoten
1
In previous UML2 versions, a multiplicity can be a set of intervals, which means that the val function is a multi-valued function. However, this complex definition has been dropped in the UML 2.x versions.
 
2
The UML 2.5.1 specification associates a qualifier with the class and property next to its visualization, e.g., with class A and property \(p_1\) in Fig. 4b. Class A is termed qualified class, and \(p_1\) is the owner property of the qualifier \(\{q_1, q_2 \}\). We introduce a different terminology, where a qualifier is associated with its semantically affected qualified property. We think that it should be visualized on the side of the qualified property (opposite to the current UML visualization).
 
3
A property denotes a multi-valued function between classes (see “Appendix B”). It corresponds to UML 2.5 binary association end, with the descriptors isUnique=true, isOrdered=false, and zero or more qualifier properties, each typed by a datatype.
 
4
Since composition denotes physical aggregation.
 
5
Since aggregation/composition denotes part-whole relationships. See “Appendix B.”
 
6
We use the same symbol as for class hierarchy. Distinction is made by context.
 
7
Note that the abstract syntax introduced in Sect. 2 does not include multiplicity constraints with gaps.
 
8
Association hierarchy (also called association inclusion) is the same as subsetting [3].
 
9
Henceforth, we identify nodes in the identification graph with the classes they represent. This convention saves introduction of a classOf mapping, and enables writing \(target(\pi )^I\) instead of \(classOf(target(\pi ))^I\).
 
10
Note that association–composition preserves the weights in cycles of the identification graph.
 
11
This abstraction heuristics reminds the abstraction rules of [23, 24], although these works have different goals.
 
12
This constraint results from the asymmetry and transitivity of part-whole relationships [71]. The UML 2.5.1 specification does not provide standard semantics to aggregation constraints, and interprets composition constraints as responsibility for existence and storage for the parts.
 
13
The more common case is that \(target(p_i^a) = source(p_{i+1}^a), i=1,n-1\), and \(\texttt {e}\in source({p_1^a})^I\), but if class extensions are not disjoint, sequences of linked objects might not follow sequences of associations in the class model.
 
14
As for aggregation, the more common case is that \(target(p_i^c) = source(p_{i+1}^c), i=1,n-1\), and \(target(q_i^c) = source(q_{i+1}^c), i=1,m-1\), but this might not be the case if class extensions can intersect.
 
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Metadaten
Titel
Removing redundant multiplicity constraints in UML class models
verfasst von
Mira Balaban
Azzam Maraee
Publikationsdatum
14.09.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Software and Systems Modeling / Ausgabe 4/2019
Print ISSN: 1619-1366
Elektronische ISSN: 1619-1374
DOI
https://doi.org/10.1007/s10270-018-0696-z

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