Mapping Cardinality-based Feature Models to Weighted Automata over Featured Multiset Semirings (Extended Version)
Robert Müller, Mathis Weiß, Malte Lochau
TL;DR
Cardinality-based feature models (CFMs) generalize Boolean feature models by allowing multiplicities, producing infinite and non-convex configuration spaces that challenge Boolean-presence-based mappings. The authors introduce weighted automata over featured multisets as a semantic bridge from CFMs to the solution space, with transitions labeled by feature multisets and weights computed via semirings (notably tropical) to map accepted words to multiset configurations. This approach is strictly more expressive than featured transition systems (FTS) and supports rich analysis through semiring theory; they implement a JAutomata-based tool and report preliminary feasibility on example models. The work enables automated reasoning about unbounded multiplicities and aggregated multiplicity constraints, offering a reusable, extensible framework for analyzing family-based variability in complex product lines and informing scalable design and procurement decisions.
Abstract
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.