Multiset Theories of Cardinality-based Feature Diagrams

Software product line engineering is a very common method for designingcomplex software systems. Feature modeling is the most common approach tospecify product lines. The main part of a feature model is a special tree offeatures called a feature diagram. Cardinality-based feature diagrams providethe most expressive tool among the current feature diagram languages. Themost common characterization of the semantics of a cardinality-based diagramis the set of flat multisets over features satisfying the constraints. However,this semantics provides a poor abstract view of the diagram. We address thisproblem by proposing another multiset theory for the cardinality-based featurediagram, called the hierarchical theory of the diagram. We show that thissemantics captures all information of the diagram so that one can retrieve thediagram from its hierarchical semantics. We also characterize sets of multisets,which can provide a hierarchical semantics of some diagrams.