  Behavioural equivalences can be characterized via bisimulation, modal logics,
and spoiler-duplicator games. In this paper we work in the general setting of
coalgebra and focus on generic algorithms for computing the winning strategies
of both players in a bisimulation game. The winning strategy of the spoiler (if
it exists) is then transformed into a modal formula that distinguishes the
given non-bisimilar states. The modalities required for the formula are also
synthesized on-the-fly, and we present a recipe for re-coding the formula with
different modalities, given by a separating set of predicate liftings. Both the
game and the generation of the distinguishing formulas have been implemented in
a tool called T-BEG.
