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Category Theory Framework for Variability Models with Non-Functional Requirements

Daniel-Jesus Munoz; Dilian Gurov; Monica Pinto; Lidia Fuentes

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Software Product Lines (SPLs) make use of Variability Models (VMs) as an input to automated reasoners, which are mainly used to generate optimal product configurations according to certain Quality Attributes (QAs). However, VMs and more specifically those including numerical features (i.e., NVMs), do not natively support QAs, and consequently, neither do automated reasoners commonly used in variability resolution. However, those satisfiability and optimisation problems have been covered and refined in other relational models such as databases.

Category Theory (CT) is an abstract mathematical theory typically used to capture the common aspects of seemingly dissimilar algebraic structures. We propose a unified relational modelling framework subsuming the structured objects of VMs and QAs and their relationships into algebraic categories. This abstraction allows a combination of automated reasoners over different domains to analyse SPLs. The solutions optimisation can now be natively performed by a combination of automated theorem proving, hashing, balanced-trees and chasing algorithms. We validate this approach by means of the edge computing SPL tool HADAS.

Munoz, Pinto and Fuentes work is supported by the European Union's H2020 research and innovation programme under grant agreement DAEMON 101017109, by the projects co-financed by FEDER funds LEIA UMA18-FEDERJA-15, MEDEA RTI2018-099213-B-I00 and Rhea P18-FR-1081 and the PRE2019-087496 grant from the Ministerio de Ciencia e Innovación.
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