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.
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