Comparative semantics of Feature Diagrams: FFD vs. vDFD

Feature Diagrams are a popular family of modelling languages used for engineering requirements in software product lines. In our previous research, we advocated the use of formal semantics as an indispensable means to clarify discussions about feature diagrams and to facilitate safe and efficient tool automation. We presented a generic formal semantics for feature diagram languages and criteria to compare them. However, other formal semantics exist. We already informally argued in favour of our semantics which, we think, is more abstract, more concise and not tool dependent. However, some of these claims needed to be further objectified. The purpose of this paper is to compare the semantics proposed by van Deursen and Klint with our own following the methodology of comparative semantics. To be made amenable to comparison, van Deursen and Klint¿s tool-based definition is first recalled and redefined by correcting some minor mistakes. Their semantics is then mapped to ours through an abstraction function. We then proceed to compare the expressiveness, embeddability and succinctness of both approaches. The study tends to confirm our semantic choices as well as our tool-independent methodology. It also demonstrates that van Deursen and Klint¿s language is fully expressive and provides various results likely to help tool developers, especially for implementing model transformations.