congruences for stochastic relations
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Date
2004-05-12
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Universität Dortmund
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Abstract
We discuss congruences for stochastic relations, stressing the equivalence of smooth equivalence relations and countably generated ó-algebras. Factor spaces are constructed for congruences and for morphisms. Semi-pullbacks are needed when investigating the interplay between congruences and bisimulations, and it is shown that semi-pullbacks exist for stochastic relations over analytic spaces, generalizing a previous result and answering an open question. Equivalent congruences are investigated, and it is shown that stochastic relations that have equivalent congruences are bisimilar. The well-known equivalence relation coming from a Hennessy-Milner logic for labelled Markov transition systems is shown to be a special case in this development.
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bisimulation, congruences, factorization, semi-pullbacks, Stochastic relations over Polish and analytic spaces