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Mathematical Techniques for Analyzing Concurrent and Probabilistic Systems
J. J. M. M. Rutten, Centrum voor Wiskunde en Informatica (CWI), Amsterdam, Netherlands, and Marta Kwiatkowska, Gethin Norman, and David Parker, University of Birmingham, England
A co-publication of the AMS and Centre de Recherches Mathématiques.

CRM Monograph Series
2004; 215 pp; hardcover
Volume: 23
ISBN-10: 0-8218-3571-8
ISBN-13: 978-0-8218-3571-5
List Price: US$69
Member Price: US$55.20
Order Code: CRMM/23
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The book consists of two sets of lecture notes devoted to slightly different methods of analysis of concurrent and probabilistic computational systems.

The first set of lectures develops a calculus of streams (a generalization of the set of natural numbers) based on the coinduction principle coming from the theory of coalgebras. It is now well understood that the interplay between algebra (for describing structure) and coalgebra (for describing dynamics) is crucial for understanding concurrent systems. There is a striking analogy between streams and formula calculus reminiscent of those appearing in quantum calculus. These lecture notes will appeal to anyone working in concurrency theory but also to algebraists and logicians.

The other set of lecture notes focuses on methods for automatically verifying probabilistic systems using techniques of model checking. The unique aspect of these lectures is the coverage of both theory and practice. The authors have been responsible for one of the most successful experimental systems for probabilistic model checking. These lecture notes are of interest to software engineers, real-time programmers, researchers in machine learning and numerical analysts who may well be interested to see how standard numerical techniques are used in a novel context.

Both sets of lectures are expository and suitable for graduate courses in theoretical computer science and for research mathematicians interested in design and analysis of concurrent and probabilistic computational systems.

Titles in this series are co-published with the Centre de Recherches Mathématiques.


Graduate students and research mathematicians interested in theoretical computer science, specifically the theory of computing models.


"Presents a new way of thinking about concurrency."

-- CMS Notes

Table of Contents

On streams and coinduction
  • Preface
  • Acknowledgments
  • Streams and coinduction
  • Stream calculus
  • Analytical differential equations
  • Coinductive counting
  • Component connectors
  • Key differential equations
  • Bibliography
Modelling and verification of probabilistic systems
  • Preface
  • Introduction
  • Discrete-time Markov chains
  • Markov decision processes
  • Continuous-time Markov chains
  • Probabilistic timed automata
  • Implementation
  • Measure theory and probability
  • Iterative solution methods
  • Bibliography
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