Progress in the behavioral analysis of software product lines at the family level benefits from further development of the underlying semantical theory. Here, we propose a behavioral equivalence for feature transition systems (FTS) generalizing branching bisimulation for labeled transition systems (LTS). We prove that branching feature bisimulation for an FTS of a family of products coincides with branching bisimulation for the LTS projection of each the individual products. For a restricted notion of coherent branching feature bisimulation we furthermore present a minimization algorithm and show its correctness. Although the minimization problem for coherent branching feature bisimulation is shown to be intractable, application of the algorithm in the setting of a small case study results in a significant speed-up of model checking of behavioral properties.

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Conference Workshop on Formal Methods and Analysis in SPL Engineering
Belder, T, ter Beek, M.H, & de Vink, E.P. (2015). Coherent branching feature bisimulation. In Electronic Proceedings in Theoretical Computer Science, EPTCS (pp. 14–30). doi:10.4204/EPTCS.182.2