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 article, 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 cardinality-based 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.