Probabilistic CEGAR 1st edtion by Holger Hermanns, Björn Wachter, Lijun Zhang ISBN 3540705437 9783540705437

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Product details:

ISBN 10:       3540705437
ISBN 13: 978-3540705437
Author:    Holger Hermanns, Björn Wachter, Lijun Zhang     

Counterexample-guided abstraction refinement (CEGAR) has been en vogue for the automatic verification of very large systems in the past years. When trying to apply CEGAR to the verification of probabilistic systems, various foundational questions arise. This paper explores them in the context of predicate abstraction.

Probabilistic CEGAR 1st Table of contents:

Chapter 1: Introduction
1.1 Overview of Counterexample-Guided Abstraction Refinement (CEGAR)
1.2 Introduction to Probabilistic Systems
1.3 Challenges in Model Checking Probabilistic Systems
1.4 Motivation for Probabilistic CEGAR
1.5 Objectives and Contributions of the Paper
1.6 Structure of the Paper

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Chapter 2: Background and Related Work
2.1 CEGAR: Principles and Overview
2.2 Model Checking in Probabilistic Systems
2.3 Probabilistic Model Checking Techniques
2.4 Probabilistic Abstraction and Refinement
2.5 Related Work on CEGAR for Probabilistic Systems
2.6 Challenges in Previous Approaches to Probabilistic CEGAR

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Chapter 3: Probabilistic Systems and Model Checking
3.1 Definition and Types of Probabilistic Systems
3.2 Markov Chains and Probabilistic Automata
3.3 Formalism for Probabilistic Systems
3.4 Probabilistic Temporal Logic and Model Checking
3.5 Verification Problems in Probabilistic Systems

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Chapter 4: Principles of Probabilistic CEGAR
4.1 Introduction to Probabilistic CEGAR
4.2 CEGAR for Probabilistic Systems: General Approach
4.3 Abstraction Techniques for Probabilistic Systems
4.4 Refinement Strategies in Probabilistic CEGAR
4.5 Comparison of Probabilistic CEGAR with Traditional CEGAR

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Chapter 5: Algorithmic Framework for Probabilistic CEGAR
5.1 Overview of the Algorithmic Framework
5.2 Steps of Probabilistic CEGAR
5.3 Initial Abstraction and Refinement Procedures
5.4 Probabilistic Counterexamples and Feedback Loops
5.5 Algorithmic Complexity and Optimization

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Chapter 6: Experimental Evaluation and Case Studies
6.1 Experimental Setup for Evaluating Probabilistic CEGAR
6.2 Case Study 1: Markov Chains in Probabilistic CEGAR
6.3 Case Study 2: Probabilistic Automata and Refinement
6.4 Performance of Probabilistic CEGAR on Real-World Systems
6.5 Comparison with Existing Approaches in Probabilistic Model Checking

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Chapter 7: Applications of Probabilistic CEGAR
7.1 Verification of Probabilistic Protocols
7.2 Application in Stochastic Systems
7.3 Probabilistic CEGAR for Reliability and Safety Verification
7.4 Use of Probabilistic CEGAR in Randomized Algorithms
7.5 Applications in Cyber-Physical Systems and Networking

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Chapter 8: Challenges and Limitations
8.1 Scalability Challenges in Probabilistic CEGAR
8.2 Dealing with Large State Spaces in Probabilistic Systems
8.3 Handling Non-determinism and Uncertainty
8.4 Accuracy and Precision of Abstraction in Probabilistic CEGAR
8.5 Limitations of Current Tools and Techniques

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Chapter 9: Open Problems and Future Directions
9.1 Open Problems in Probabilistic CEGAR
9.2 Extensions to Non-Markovian and Hybrid Probabilistic Systems
9.3 Improving the Efficiency of Abstraction and Refinement
9.4 Integration of Probabilistic CEGAR with Other Verification Techniques
9.5 Potential Applications in New Domains (e.g., AI, Autonomous Systems)

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Chapter 10: Conclusion
10.1 Summary of Contributions
10.2 Impact of Probabilistic CEGAR on Model Checking
10.3 Final Thoughts on the Future of Probabilistic Model Checking
10.4 Concluding Remarks

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