Modal Characterisations of Probabilistic and Fuzzy Bisimulations

                    Yuxin Deng and Hengyang Wu

This paper aims to investigate bisimulation on fuzzy systems. Forthat purpose 
we revisit bisimulation in the model of reactive probabilistic processes with 
countable state spaces and obtain two findings: (1) bisimilarity coincides with
 simulation equivalence, which generalises a result on finite-state processes 
originally established by Baier; (2) the modal characterisation of bisimilarity
 by Desharnais et al. admits a much simpler completeness proof. Furthermore, 
inspired by the work of Hermanns et al. on probabilistic systems, we provide 
a sound and complete modal characterisation of fuzzy bisimilarity.