Mathematical techniques for analyzing concurrent and probabilistic systems

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Mathematical techniques for analyzing concurrent and probabilistic systems / J.J.M.M. Rutten ... [et al.] ; Prakash Panangaden, Franck van Breugel, editors

資料種別:

図書

出版情報:

Providence, R.I. : American Mathematical Society, c2004

形態:

viii, 215 p. ; 26 cm

シリーズ名:

CRM monograph series ; v. 23 <BA19947059>

著者名:

ISBN:

9780821835715 [0821835718]

書誌ID:

BA66610163

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

その他の標題:

Concurrent and probabilistic systems

注記:

Includes bibliographical references (p. 209-215)

主題:

System analysis

言語:

英語

目次情報:

Preface

On Streams and Coinduction

Acknowledgments

Streams and Coinduction / Chapter 1.：

Streams / 1.1.：

Proofs by Coinduction / 1.2.：

Definitions by Coinduction / 1.3.：

Examples of Coinductive Proofs / 1.4.：

Coinduction and Greatest Fixed Points / 1.5.：

Other Coalgebras / 1.6.：

Discussion / 1.7.：

Stream Calculus / Chapter 2.：

Behavioural Differential Equations / 2.1.：

Basic Stream Calculus / 2.2.：

Coinduction-Up-To / 2.3.：

Basic Properties / 2.4.：

Infinite Sum / 2.5.：

Solving Behavioural Differential Equations / 2.6.：

Solving Difference Equations / 2.7.：

Streams and Weighted Automata / 2.8.：

Rational Streams / 2.9.：

Streams and Languages / 2.10.：

Analytical Differential Equations / 2.11.：

Shuffle Product and Shuffle Inverse / 3.1.：

Stream Exponentiation / 3.2.：

Comparing Convolution and Shuffle Product / 3.3.：

Solving Analytical Differential Equations / 3.4.：

Coinductive Counting / 3.5.：

Introduction / 4.1.：

Compositions of Natural Numbers / 4.2.：

Surjections / 4.3.：

Counting with Probabilities / 4.4.：

Well-Bracketed Words / 4.5.：

Streams and Continued Fractions / 4.6.：

More on Well-Bracketed Words / 4.7.：

Permutations / 4.8.：

Set Partitions / 4.9.：

Special Numbers / 4.10.：

Component Connectors / 4.11.：

Timed Data Streams / 5.1.：

Basic Connectors: Channels / 5.3.：

More Channels and the Merge Connector / 5.4.：

Composing Connectors / 5.5.：

Connector Equivalence / 5.6.：

Protocol Verification / 5.7.：

Key Differential Equations / 5.8.：

Bibliography

Modelling and Verification of Probabilistic Systems

Acknowledgements

Motivation

The models

Properties of Interest

Probabilistic Model Checking and Other Analysis Methods

Discrete-Time Markov Chains

Paths and Probability Measures

Probabilistic Computation Tree Logic (PCTL)

PCTL Model Checking

Case Study: The IPv4 ZeroConf Protocol

Markov Decision Processes

Fairness

Case Study: Self-Stabilisation Algorithms / 3.6.：

Continuous-Time Markov Chains / 3.7.：

Steady-State and Transient Behaviour

Continuous Stochastic Logic (CSL)

CSL Model Checking

Complexity of CSL Model Checking

Case Study: Dynamic Power Management

Probabilistic Timed Automata

Time, Clocks and Zones

Syntax of Probabilistic Timed Automata

Parallel Composition

Semantics of Probabilistic Timed Automata

Probabilistic Timed Computation Tree Logic (PTCTL)

Model Checking: The Region Graph Approach

Model Checking: The Digital Clocks Approach

Case Study: IEEE 1394 FireWire Root Contention

Implementation / 5.9.：

Sparse Matrices / 6.1.：

Multi-Terminal Binary Decision Diagrams / 6.3.：

Model Representation with MTBDDs / 6.4.：

MTBDD-Based Model Checking / 6.5.：

Measure Theory and Probability / 6.6.：

Iterative Solution Methods / Appendix B.：

The Jacobi Method / B.1.：

The Gauss-Seidel Method / B.2.：

Over-Relaxation Methods / B.3.：

Preface

On Streams and Coinduction

Acknowledgments

Streams and Coinduction / Chapter 1.：

Streams / 1.1.：

Proofs by Coinduction / 1.2.：

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