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Stochastic Relations Foundations for Markov Transition Systems
Article Type: Book reports From: Kybernetes, Volume 37, Issue 3/4.
Stochastic Relations Foundations for Markov Transition SystemsErnst-Erich DoberkatChapman and Hall/CRC2007 (June)£56.99 ($99.95)368 pp.ISBN 978-1-58488-941-0Keywords: Cybernetics, Informatics, Systems
This is part of the new series by the publishers on “Studies in informatics”. In brief it develops the theory of stochastic relations as a basis for Markov transition systems. It aims to summarise previous contributions that are only available by searching numerous references in the literature. It also highlights the author's own researches.
Its most important features are given as:
.Provides a self-contained introduction to Polish and analytic spaces, measures, selection theorems, and categories, including monads and Eilenberg-Moore algebras.
.Examines the interplay between probability theory and coalgebras.
.Presents a systematic treatment of the categorical aspects of the probability theory for Markov transition systems.
.Investigates bisimulations and logical and behavioral equivalence, promoting a better understanding of nondeterministic and randomized process.
.Studies probabilistic interpretations of modal and temporal logics.
.Includes case studies of software architecture, the converse of a stochastic relation, and the average case analysis of two algorithms.
Note that the author views developments from the general theory of coalgebras in the context of the subprobability function. The book contains numerous problems and several case studies.
It claims to be an invaluable study of this important theory.