Probabilistic bisimulation
Since the seminal paper [1] probabilistic process algebra has been
studied. For strong bisimulation there is concensus as what comprises
strong bisimilarity. For the weak case, there is little agreement
which definition is the most appropriate. Crafa and Ranzato [2] seek
to abstract away from the probabilistic setting as to see what happens
when probabilistic choice is simplified to non-deterministic
choice. The aim is to compare the various examples that are
characteristic for the different approaches, e.g. [3] and [4], from
this perspective in order to catalogue the multitude of ideas.
[1] R.J. van Glabbeek, S.A. Smolka, B.Steffen, C.M.N. Tofts, Reactive,
Generative, and Stratified Models of Probabilistic Processes,
Proc. LICS, Philadelphia, 1990, pages 130-141.
[2] S. Crafa and F. Ranzato: Logical Characterizations of Behavioral
Relations on Transition Systems of Probability Distributions. ACM
Transactions on Computational Logic 16(1), 2014, pages 2:1-2:24.
[3] E. Bandini, R. Segala, Axiomatizations for Probabilistic
Bisimulation, Proc. ICALP 2001, Crete, pages 370-381.
[4] C. Eisentraut, H. Hermanns, J. Krämer, A. Turrini, Lijun Zhang,
Deciding Bisimilarities on Distributions, Proc. QEST 2013, Buenos
Aires, pages 72-88.