Unprovability of the Logical Characterization of Bisimulation

Details Unprovability of the Logical Characterization of Bisimulation Unprovability of the Logical Characterization of Bisimulation

2010-05-27

arxiv.org/abs/1005.5142v3

Computer Science

Logic in Computer Science

Extended introduction and comments; extra section on semi-pullbacks; 11 pages Some background details added; extra example on

Scientific paper

We quickly review labelled Markov processes (LMP) and provide a counterexample showing that in general measurable spaces, event bisimilarity and state bisimilarity differ in LMP. This shows that the logic in Desharnais [*] does not characterize state bisimulation in non-analytic measurable spaces. Furthermore we show that, under current foundations of Mathematics, such logical characterization is unprovable for spaces that are projections of a coanalytic set. Underlying this construction there is a proof that stationary Markov processes over general measurable spaces do not have semi-pullbacks. ([*] J. Desharnais, Labelled Markov Processes. School of Computer Science. McGill University, Montr\'eal (1999))

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