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arXiv · 1005.5142

Unprovability of the Logical Characterization of Bisimulation

Pedro Sánchez Terraf
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Abstract

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, Montréal (1999))

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Pedro Sánchez Terraf. 2010-12-10. Unprovability of the Logical Characterization of Bisimulation. https://arxiv.org/abs/1005.5142

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