The Semantics of Feature Models via Formal Languages

Feature modeling is a common framework for software design. A feature model is a graphical structure presenting a hierarchical decomposition of features, called a feature diagram, with some possible crosscutting constraints between them. Feature modeling languages are grouped into basic and cardinality-based feature models. Cardinalitybased feature models subsume basic ones. In this paper, we provide a reduction process, which allows us to go from a cardinality-based feature diagram to an appropriate regular expression such that the expression faithfully captures the semantics of the feature diagram. As for CCs, we propose a formal language interpretation of them. In this way, we provide a formal language-based semantics for cardinality-based feature models. Accordingly, we describe a computational hierarchy of feature models, which guides us in how feature models can be constructively analyzed. We also characterize some existing analysis operations over feature models in terms of on languages and discuss the corresponding decidability problems.