Linear Software Models: Equivalence of Modularity Matrix to Its Modularity Lattice

Iaakov Exman; Daniel Speicher

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Paper

Linear Software Models: Equivalence of Modularity Matrix to Its Modularity Lattice

Topics: Model Analysis and Checking; Model Composition

In Proceedings of the 10th International Conference on Software Paradigm Trends - Volume 0ICSOFT, 109-116, 2015 , Colmar, Alsace, France

Authors: Iaakov Exman ¹ and Daniel Speicher ²

Affiliations: ¹ JCE - The Jerusalem College of Engineering, Israel ; ² University of Bonn, Germany

Keyword(s): Linear Software Models, Modularity Matrix, Modularity Lattice, Formal Concept Analysis, Equivalence.

Related Ontology Subjects/Areas/Topics: Model Analysis and Checking ; Model Composition ; Models ; Paradigm Trends ; Software Engineering

Abstract: Modularity is an important feature to solve the composition problem of software systems from subsystems. Recently it has been shown that Software systems’ Modularity Matrices linking structors to functionals can be put in almost block-diagonal form, where blocks reveal higher-level software modules. An alternative formalization has been independently proposed using Conceptual Lattices linking attributes to objects. But, are these independent formalizations related? This paper shows the equivalence of Modularity Matrices to their respective Modularity Lattices. Both formalizations support the simplest form of software composition, i.e. linear composition, expressed as an addition of independent components. This equivalence has both theoretical and practical advantages. These are illustrated by comparison of both representations for a series of case studies.

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Paper citation in several formats:

Exman, I. and Speicher, D. (2015). Linear Software Models: Equivalence of Modularity Matrix to Its Modularity Lattice. In Proceedings of the 10th International Conference on Software Paradigm Trends (ICSOFT 2015) - ICSOFT-PT; ISBN 978-989-758-115-1, SciTePress, pages 109-116. DOI: 10.5220/0005557701090116

@conference{icsoft-pt15,
author={Iaakov Exman. and Daniel Speicher.},
title={Linear Software Models: Equivalence of Modularity Matrix to Its Modularity Lattice},
booktitle={Proceedings of the 10th International Conference on Software Paradigm Trends (ICSOFT 2015) - ICSOFT-PT},
year={2015},
pages={109-116},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005557701090116},
isbn={978-989-758-115-1},
}

TY - CONF

JO - Proceedings of the 10th International Conference on Software Paradigm Trends (ICSOFT 2015) - ICSOFT-PT
TI - Linear Software Models: Equivalence of Modularity Matrix to Its Modularity Lattice
SN - 978-989-758-115-1
AU - Exman, I.
AU - Speicher, D.
PY - 2015
SP - 109
EP - 116
DO - 10.5220/0005557701090116
PB - SciTePress