We introduce a generalization of the bisimulation game that finds distinguishing Hennessy-Milner logic formulas from every finitary, subformula-closed language in van Glabbeek's linear-time--branching-time spectrum between two finite-state processes. We identify the relevant dimensions that measure expressive power to yield formulas belonging to the coarsest distinguishing behavioral preorders and equivalences; the compared processes are equivalent in each coarser behavioral equivalence from the spectrum. We prove that the induced algorithm can determine the best fit of (in)equivalences for a pair of processes.

@article{paperbot1668,
  title = {Deciding All Behavioral Equivalences at Once: A Game for Linear-Time--Branching-Time Spectroscopy},
  author = {Benjamin Bisping and David N. Jansen and Uwe Nestmann},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 18, Issue 3},
  year = {2022},
  doi = {10.46298/lmcs-18(3:19)2022}
}