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 translation 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.