One Energy Game for the Spectrum between Branching Bisimilarity and Weak Trace Semantics

We provide the first generalized game characterization of van Glabbeek's linear-time--branching-time spectrum with silent steps. Thereby, one multi-dimensional energy game can be used to characterize and decide a wide array of weak behavioral equivalences between stability-respecting branching bisimilarity and weak trace equivalence in one go. To establish correctness, we relate attacker-winning energy budgets and distinguishing sublanguages of Hennessy--Milner logic that we characterize by eight dimensions of formula expressiveness.