Feature Diagrams and Logics: There and Back Again

Feature modeling is a notation and an approach for modeling
commonality and variability in product families. In their basic form,
feature models contain mandatory/optional features, feature groups,
and implies and excludes relationships. It is known that such feature
models can be translated into propositional formulas, which enables
the analysis and configuration using existing logic-based tools. In
this paper, we consider the opposite transla- tion problem, that is,
the extraction of feature models from propositional formulas. We give
an automatic and efficient procedure for computing a feature model
from a formula. As a side effect we characterize a class of logical
formulas equivalent to feature models and identify logical structures
corresponding to their syntactic elements. While many different
feature models can be extracted from a single formula, the computed
model strives to expose graphically the maximum of the original
logical structure while minimizing redundancies in the representation.
The presented work furthers our understanding of the semantics of
feature modeling and its relation to logics, opening avenues for new
applications in reverse engineering and refactoring of feature models.