A metrized duality theorem for Markov processes

Kozen, Dexter and Mardare, Radu and Panangaden, Prakash (2014) A metrized duality theorem for Markov processes. Electronic Notes in Theoretical Computer Science, 308. pp. 211-227. ISSN 1571-0661 (https://doi.org/10.1016/j.entcs.2014.10.012)

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We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the way to developing theories of approximate reasoning for probabilistic systems.