**CRM Monograph Series**

Volume: 23;
2004;
215 pp;
Hardcover

MSC: Primary 68;

**Print ISBN: 978-0-8218-3571-5
Product Code: CRMM/23**

List Price: $74.00

AMS Member Price: $59.20

MAA Member Price: $66.60

**Electronic ISBN: 978-1-4704-3867-8
Product Code: CRMM/23.E**

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

#### Supplemental Materials

# Mathematical Techniques for Analyzing Concurrent and Probabilistic Systems

Share this page *Editors and Authors: *
*Prakash Panangaden; Franck van Breugel; J. J. M. M. Rutten; Marta Kwiatkowska; Gethin Norman; David Parker*

A co-publication of the AMS and Centre de Recherches Mathématiques

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.

#### Readership

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

#### Reviews & Endorsements

Presents a new way of thinking about concurrency.

-- CMS Notes

#### Table of Contents

# Table of Contents

## Mathematical Techniques for Analyzing Concurrent and Probabilistic Systems

- Cover Cover11
- Title page i2
- Contents iii4
- Preface vii8
- On streams and coinduction 110
- Preface 312
- Acknowledgments 514
- Streams and coinduction 716
- Stream calculus 1524
- Analytical differential equations 3746
- Coinductive counting 5160
- Component connectors 7382
- Appendix A. Key differential equations 8998
- Bibliography 91100
- Modelling and verification of probabilistic systems 93102
- Preface 95104
- Introduction 97106
- Discrete-time Markov chains 101110
- Markov decision processes 117126
- Continuous-time Markov chains 137146
- Probabilistic timed automata 155164
- Implementation 181190
- Appendix A. Measure theory and probability 203212
- Appendix B. Iterative solution methods 205214
- Bibliography 209218
- Back Cover Back Cover1225