Stochastic Relations

Stochastic Relations : Foundations for Markov Transition Systems

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Description

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.show more

Product details

  • Electronic book text | 376 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 1000 equations; 16 Illustrations, black and white
  • 158488942X
  • 9781584889427

Table of contents

Preface A Gentle Tutorial to All Things Considered Introduction Measurable Spaces Polish and Analytic Spaces Measurable Selectors Probability Measures Categories Stochastic Relations as Monads Introduction The Manes Monad The Giry Monad Case Study: Architectural Modeling through Monads Eilenberg-Moore Algebras for Stochastic Relations Introduction Characterization through Equivalence Relations Positive Convex Structures Algebras through Positive Convex Structures Examples The Left Adjoint The Existence of Semi-Pullbacks Introduction A Road Map Extending Semi-Pullbacks of Measures The Existence of Semi-Pullbacks Congruences and Bisimulations Introduction Smooth Equivalence Relations Factoring Bisimulations Behavioral Equivalence and a Portmanteau 2-Bisimulations Simple Relations Case Study: The Converse of a Stochastic Relation Case Study: Simple Relations for Counting Interpreting Modal and Temporal Logics Introduction Modal Logics Projective Limits for Interpreting Temporal Logics F-Bisimulations for CSL Logical Equivalence for μCSL Appendix: Notations Categories Spaces Other Bibliography Index Bibliographic Notes appear at the end of each chapter.show more