Stochastic Relations: Foundations for Markov Transition Systems [Paperback]

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.Introduction. A Gentle Tutorial to All Things Considered. Stochastic Relations as Monads. EilenbergMoore Algebras for Stochastic Relations. The Existence of Semi-Pullbacks. Congruences and Bisimulations. Interpreting Modal and Temporal Logics. Appendix. Bibliography. Index.This book 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, it examines congruences and morphisms. It applies these topics to the monoidal structure, and defines bisimilarity and behavioral equivalence within this framework. Developments from the general theory of coalgebras in the context of the subprobability functor are presented. The book also includes case studies of software architecture, the converse of a stochastic relation, and the average case analysis of two algorithms.US? 2007 by Taylor & Francis Group, LLC