Multiset Theories of Cardinality-based Feature Diagrams

TL;DR

This paper introduces a hierarchical multiset theory for cardinality-based feature diagrams in software product line engineering, providing a more expressive semantics that captures all diagram information.

Contribution

It proposes a new hierarchical semantics for feature diagrams that overcomes limitations of the existing flat multiset semantics, enabling complete diagram retrieval.

Findings

Hierarchical semantics captures all diagram information.

The new theory allows diagram reconstruction from semantics.

Characterization of multiset sets suitable for hierarchical semantics.

Abstract

Software product line engineering is a very common method for designing complex software systems. Feature modeling is the most common approach to specify product lines. The main part of a feature model is a special tree of features called a feature diagram. Cardinality-based feature diagrams provide the most expressive tool among the current feature diagram languages. The most common characterization of the semantics of a cardinality-based diagram is the set of flat multisets over features satisfying the constraints. However, this semantics provides a poor abstract view of the diagram. We address this problem by proposing another multiset theory for the cardinality-based feature diagram, called the hierarchical theory of the diagram. We show that this semantics captures all information of the diagram so that one can retrieve the diagram from its hierarchical semantics. We also characterize sets of multisets, which can provide a hierarchical semantics of some diagrams.