## Stochastic Relations: Foundations for Markov Transition SystemsCollecting information previously scattered throughout the vast literature, including the author's own research, Stochastic Relations: Foundations for Markov Transition Systems develops the theory of stochastic relations as a basis for Markov transition systems. After an introduction to the basic mathematical tools from topology, measure |

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### Contents

A Gentle Tutorial to All Things Considered | 1 |

Stochastic Relations as Monads | 83 |

EilenbergMoore Algebras for Stochastic Relations | 131 |

The Existence of SemiPullbacks | 157 |

Congruences and Bisimulations | 179 |

Interpreting Modal and Temporal Logics | 251 |

Notations | 327 |

331 | |

339 | |

### Other editions - View all

Stochastic Relations: Foundations for Markov Transition Systems Ernst-Erich Doberkat No preview available - 2007 |

Stochastic Relations: Foundations for Markov Transition Systems Ernst-Erich Doberkat No preview available - 2019 |

### Common terms and phrases

2-bisimulation analytic sets analytic spaces architecture assume atomic propositions behavioral equivalence bisimilar bisimulations Borel map Borel measurable Borel sets characterization closed set coalgebras component computations Consequently construction continuous map converse COROLLARY countable cylinder sets defined DEFINITION diagram discussion Eilenberg-Moore algebras element established exists factor spaces functions Giry monad given graph hence holds implies induction input invariant Borel sets investigated Kripke models Lemma Let f logical equivalence map f measurable map measurable space measurable subset metric space modal logics modal operator monad morphism morphism f natural transformation node nondeterministic nontrivial O-algebra open sets path formula PF-system Polish space positive convex structure probabilistic probability measures projective limit proof properties resp Section semi-pullback sequence smooth equivalence relations stochastic relation subprobability functor surjective Theorem topology transition variable

### Popular passages

Page 334 - HENNESSY, M., AND MILNER, R. (1980),. On observing nondeterminism and concurrency, in "Automata, Languages, and Programming.