On logical and extensional characterizations of attributed feature models

Highlights

• We study the logical and extensional representations of feature models.

• We study the logical and extensional representations of attributed feature models.

• We investigate the algebraic properties of operations and relations on the extensional representations of both models.

• We identify the logical counterpart of the above relations and operations for both basic and attributed feature models.

• We show that these operations and relations have meaning in lattices.

Abstract

Software-intensive systems can have thousands of interdependent configuration options across different subsystems. Feature models (FMs) allow designers to organize the configuration space by describing configuration options using interdependent features: a feature is a name representing some functionality and each software variant is identified by a set of features. Attributed feature models (AFMs) extend FMs to describe the, possibly constrained, choice of a value from domains such as integers or strings: each attribute is associated to one feature, and when the feature is selected then the attribute brings some additional information relative to the selected features. Different representations of FMs and AFMs have been proposed in the literature. In this paper we focus on the logical representation (which works well in practice) and the extensional representation (which has been recently shown well suited for theoretical investigations). We provide an algebraic and a logical characterization of operations and relations on FMs and AFMs, and we formalize the connection between the two characterizations as monomorphisms from lattices of logical FMs and AFMs to lattices of extensional FMs and AFMs, respectively. This formalization sheds new light on the correspondence between the algebraic and logical characterizations of operations and relations for FMs and AFMs. It aims to foster the development of a formal framework for supporting practical exploitation of future theoretical developments on FMs, AFMs and multi software product lines.

Introduction

Software-intensive systems can have thousands of interdependent configuration options across different subsystems. In the resulting configuration space, different software variants can be obtained by selecting among these configuration options and accordingly assembling the underlying subsystems. The interdependencies between options are dictated by corresponding interdependencies between the underlying subsystems [1].

Feature models (FMs) [2] allow developers to organize the configuration space and facilitate the construction of software variants by describing configuration options using interdependent features [3]: a feature is a name representing some functionality, a set of features is called a configuration, and each configuration that fulfills the interdependencies expressed by the FM, called a product, identifies a software variant.

Attributed feature models (AFMs) [4] extend FMs to describe the, possibly constrained, choice of a value from domains such as integers or strings. Each attribute is associated to one feature, and if the feature is selected then the attribute brings some additional information relative to the product (identified by selected features). For instance, an “SSD memory” feature may have a “capacity” attribute that should be set to a value greater than 512 GB whenever the feature “pro” is selected.

Software-intensive systems can comprise thousands of features and several subsystems [5], [6], [7], [8]. The design, development and maintenance of FMs with thousands of features can be simplified by representing large FMs as sets of smaller interdependent FMs [6], [9] that we call fragments. To this aim, several representations of FMs have been proposed in the literature (see, e.g., Batory [2] and Sect. 2.3 of Apel et al. [1]) and many approaches for composing FMs from fragments have been investigated [10], [11], [12], [13], [14].

In this paper we focus on the logical representation (which works well in practice [15], [16], [17]) and the extensional representation (which has been recently shown well suited for theoretical investigations [18], [19]).

The starting point of this investigation is a novel partial order between FMs, that we call the FM fragment relation. It is induced by a notion of FM composition that has been used to model industrial-size configuration spaces [18], [19], such as the configuration space of the Gentoo source-based Linux distribution [20], that consists of many configurable packages (the March 1st 2019 version of the Gentoo distribution comprises 671617 features spread across 36197 FMs). We exploit this partial order to provide an algebraic characterization of operations and relations on FMs and AFMs. Then, we provide a logical characterizations of them and formalize the connection between the two characterizations as monomorphisms from lattices of logical FMs and AFMs to lattices of extensional FMs and AFMs, respectively. This paper is an extended version of prior work [21] which does not consider AFMs.

The remainder of this paper is organized as follows. In Section 2 we recollect the necessary background and introduce the fragment relation for FMs and AFMs. In Section 3 we present the algebraic characterization of operations and relations on FMs and AFMs. In Section 4 we present the logical characterization of the operations and relations on FMs together with a formal account of the connection with the algebraic characterization, and in Section 5 we extend these results to AFMs. We discuss related work in Section 6, and conclude the paper in Section 7 by outlining planned future work.

The material about FMs and AFMs is presented in distinct sections, all the sections about FMs or AFMs contain “FM” or “AFM” in the title, and the sections about FMs do not depend on the sections about AFMs. So, a reader may decide to first consider the material on FMs and then the extension to AFMs.