Category Theory Framework for Variability Models with Non-functional Requirements

Abstract

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.

Quality-aware analysis and optimisation of virtual network functions

“…SPL Conqueror supports them only partially by calculating an approximated value for the feature attributes based on the set of measured configurations during the generation of the product configuration. Our CT framework [35] supports both the feature-level and configuration-level QAs.…”

“…In some cases, a declarative solver is also used, as in the SATIBEA algorithm, which is defined as a combination of an SAT solver and the IBEA genetic algorithm and the GIA algorithm that uses a Z3 solver. In [35], authors discuss the benefits and drawbacks of approaches to defining an external quality model with two important conclusions: (1) most existing solutions are not directly compatible with automated quality-reasoning, and (2) SPL reasoning lacks a "unified" model that appropriately supports quality metrics. STEAM uses abduction and deduction reasoning.…”

“…In [35], we detail a CT framework that unifies numerical VMs with QAs as a category where features and QAs are objects, and data types, hierarchical relationships, and quality and feature constraints are arrows. We use this model to represent SPLs as categories.…”

“…With the objective of modelling and reasoning flexibility, we proposed a Category Theory (CT) [3] framework for SPLs. There, we unified FMs and Quality Models (QMs) [35] in a single model and tool. It has the potential to support complex relationships and the quality-reasoning of numerical FMs.…”

“…Additionally, we define and implement in our CT framework the necessary reasoning algorithms in Section 3. For the evaluation Section 5, we selected the 4 most complete tools: CQL IDE [35], ClaferMoo [39], AAFM Python Framework [18], and SATIBEA [23]. Alongside our new CT reasoning algorithms, we validated those tools for 5 different real-world SPLs with different QAs and a variety of reasoning operations of the three groups.…”