Resource bisimilarity and graded bisimilarity coincide

Resource bisimilarity has been proposed in the literature on concurrency theory as a notion of bisimilarity over labeled transition systems that takes into account the number of choices that a system has. Independently, g-bisimilarity has been defined over Kripke models as a suitable notion of bisimilarity for graded modal logic. This note shows that these two notions of bisimilarity coincide over image-finite Kripke frames.

Research highlights
► Resource bisimilarity coincides with graded bisimilarity.
► The Hennessy–Milner property holds for graded modal logic over the class of image-finite Kripke frames modulo graded bisimilarity.
► Resource bisimilarity on multiframes coincides with coalgebraic bisimilarity for the finite multiset functor.