Proving Conditional Termination 1st edition by Byron Cook, Sumit Gulwani, Tal Lev Ami, Andrey Rybalchenko, Mooly Sagiv ISBN 3540705437 9783540705437

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Product details:

ISBN 10:       3540705437
ISBN 13: 978-3540705437
Author:         Byron Cook, Sumit Gulwani, Tal Lev-Ami, Andrey Rybalchenko, Mooly Sagiv

We describe a method for synthesizing reasonable underapproximations to weakest preconditions for termination—a long-standing open problem. The paper provides experimental evidence to demonstrate the usefulness of the new procedure.

Proving Conditional Termination 1st  Table of contents:

Chapter 1: Introduction
1.1 Overview of Termination Analysis
1.2 Conditional Termination and Its Importance
1.3 Challenges in Proving Conditional Termination
1.4 Objectives and Contributions of the Paper
1.5 Structure of the Paper

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Chapter 2: Background and Related Work
2.1 Termination in Program Analysis
2.2 Conditional Termination: Definitions and Examples
2.3 Formal Methods for Termination Proofs
2.4 Previous Approaches to Conditional Termination
2.5 Key Tools and Techniques in Termination Analysis

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Chapter 3: Formalization of Conditional Termination
3.1 Defining Conditional Termination
3.2 Mathematical Models for Conditional Termination
3.3 Relation to Standard Termination Proofs
3.4 Termination Under Different Conditions
3.5 Criteria for Conditional Termination

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Chapter 4: Proving Conditional Termination
4.1 Proof Techniques for Conditional Termination
4.2 Using Well-founded Relations in Termination Proofs
4.3 The Role of Invariants in Conditional Termination
4.4 Automated Approaches to Conditional Termination
4.5 Case Study: Proving Conditional Termination in a Simple Program

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Chapter 5: Methods for Conditional Termination Verification
5.1 Static Analysis for Conditional Termination
5.2 Abstract Interpretation and Conditional Termination
5.3 Model Checking Approaches for Termination
5.4 Symbolic Execution in Termination Verification
5.5 Combining Verification Techniques for Conditional Termination

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Chapter 6: Case Studies and Applications
6.1 Conditional Termination in Recursive Functions
6.2 Analyzing Termination in Concurrent Programs
6.3 Conditional Termination in Loops and Conditional Statements
6.4 Application in Formal Verification of Software Systems
6.5 Case Study: Verifying Conditional Termination in a Real-World System

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Chapter 7: Challenges in Proving Conditional Termination
7.1 Complexity of Conditional Termination Proofs
7.2 Handling Non-determinism in Conditional Termination
7.3 Dealing with Loops and Recursion
7.4 Scalability Issues in Conditional Termination Verification
7.5 Unsolved Problems and Future Directions in Termination Proofs

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Chapter 8: Advanced Topics
8.1 Conditional Termination in Non-Deterministic Systems
8.2 Termination in Probabilistic and Stochastic Systems
8.3 Termination in Real-Time and Hybrid Systems
8.4 Automated Tools for Conditional Termination Analysis
8.5 Beyond Conditional Termination: Generalized Termination Proofs

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Chapter 9: Performance and Optimization
9.1 Optimizing Termination Proofs for Large Systems
9.2 Efficiency of Proof Techniques for Conditional Termination
9.3 Memory and Computational Complexity in Verification
9.4 Benchmarking Conditional Termination Methods
9.5 Improving Performance of Termination Analysis Tools

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Chapter 10: Conclusion
10.1 Summary of Conditional Termination Proofs
10.2 Key Contributions and Findings of the Paper
10.3 Impact on Software Verification and Formal Methods
10.4 Future Directions and Research in Conditional Termination
10.5 Final Remarks

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