Formalizing cardinality-based feature models and their specialization

Feature modeling is an important approach to capture the commonalities and variabilities in system families and product lines. Cardinality-based feature modeling integrates a number of existing extensions of the original feature-modeling notation from Feature-Oriented Domain Analysis. Staged configuration is a process that allows the incremental configuration of cardinality-based feature models. It can be achieved by performing a step-wise specialization of the feature model. In this paper, we argue that cardinality-based feature models can be interpreted as a special class of context-free grammars. We make this precise by specifying a translation from a feature model into a context-free grammar. Consequently, we provide a semantic interpretation for cardinalitybased feature models by assigning an appropriate semantics to the language recognized by the corresponding grammar. Finally, we give an account on how feature model specialization can be formalized as transformations on the grammar equivalent of feature models.