Description

Book Synopsis

Collecting 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 theory, and categories, the book examines the central topics of congruences and morphisms, applies these to the monoidal structure, and defines bisimilarity and behavioral equivalence within this framework. The author views developments from the general theory of coalgebras in the context of the subprobability functor. These tools show that bisimilarity and behavioral and logical equivalence are the same for general modal logics and for continuous time stochastic logic with and without a fixed point operator.

With numerous problems and several case studies, this book is an invaluable study of an important aspect of computer science theory.



Table of Contents
Introduction. A Gentle Tutorial to All Things Considered. Stochastic Relations as Monads. Eilenberg–Moore Algebras for Stochastic Relations. The Existence of Semi-Pullbacks. Congruences and Bisimulations. Interpreting Modal and Temporal Logics. Appendix. Bibliography. Index.

Stochastic Relations: Foundations for Markov

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    A Hardback by Ernst-Erich Doberkat

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      Book details

      Publisher Chapman & Hall/CRC
      Published 17 May 2007
      ISBN-13 9781584889410
      978-1584889410
      ISBN-10 1584889411
      Also in:
      Stochastics

      Description

      Book Synopsis

      Collecting 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 theory, and categories, the book examines the central topics of congruences and morphisms, applies these to the monoidal structure, and defines bisimilarity and behavioral equivalence within this framework. The author views developments from the general theory of coalgebras in the context of the subprobability functor. These tools show that bisimilarity and behavioral and logical equivalence are the same for general modal logics and for continuous time stochastic logic with and without a fixed point operator.

      With numerous problems and several case studies, this book is an invaluable study of an important aspect of computer science theory.



      Table of Contents
      Introduction. A Gentle Tutorial to All Things Considered. Stochastic Relations as Monads. Eilenberg–Moore Algebras for Stochastic Relations. The Existence of Semi-Pullbacks. Congruences and Bisimulations. Interpreting Modal and Temporal Logics. Appendix. Bibliography. Index.

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