Mapping Cardinality-based Feature Models to Weighted Automata over Featured Multiset Semirings

Cardinality-based feature models permit to select multiple copies of the same feature, thus generalizing the notion of product configurations from subsets of Boolean features to multisets of feature instances. This increased expressiveness shapes a-priori infinite and non-convex configuration spaces, which renders established solution-space mappings based on Boolean presence conditions insufficient for cardinality-based feature models. To address this issue, we propose weighted automata over featured multiset semirings as a novel behavioral variability modeling formalism for cardinality-based feature models. The formalism uses multisets over features as a predefined semantic domain for transition weights. It permits to use any algebraic structure forming a proper semiring on multisets to aggregate the weights traversed along paths to map accepted words to multiset configurations. In particular, tropical semirings constitute a promising sub-class with a reasonable trade-off between expressiveness and computational tractability of canonical analysis problems. The formalism is strictly more expressive than featured transition systems, as it enables upper-bound multiplicity constraints depending on the length of words. We provide a tool implementation of the behavioral variability model and present preliminary experimental results showing applicability and computational feasibility of the proposed approach.