A Numerical Abstract Domain Based on Expression Abstraction and Max Operator with Application in Timing Analysis 1st edtion by Bhargav Gulavani, Sumit Gulwani ISBN 3540693888 9783540693888

A Numerical Abstract Domain Based on Expression Abstraction and Max Operator with Application in Timing Analysis 1st edtion by Bhargav S. Gulavani, Sumit Gulwani – Ebook PDF Instant Download/Delivery. 3540693888, 978-3540693888
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ISBN 10:       3540693888
ISBN 13: 978-3540693888
Author:         Bhargav S. Gulavani, Sumit Gulwani

This paper describes a precise numerical abstract domain for use in timing analysis. The numerical abstract domain is parameterized by a linear abstract domain and is constructed by means of two domain lifting operations. One domain lifting operation is based on the principle of expression abstraction (which involves defining a set of expressions and specifying their semantics using a collection of directed inference rules) and has a more general applicability. It lifts any given abstract domain to include reasoning about a given set of expressions whose semantics is abstracted using a set of axioms. The other domain lifting operation incorporates disjunctive reasoning into a given linear relational abstract domain via introduction of max expressions. We present experimental results demonstrating the potential of the new numerical abstract domain to discover a wide variety of timing bounds (including polynomial, disjunctive, logarithmic, exponential, etc.) for small C programs.

A Numerical Abstract Domain Based on Expression Abstraction and Max Operator with Application in Timing Analysis 1st Table of contents:

Chapter 1: Introduction
1.1 Overview of Numerical Abstract Domains
1.2 Expression Abstraction and its Importance
1.3 Max Operator in Abstract Interpretation
1.4 Relevance of the Proposed Domain in Timing Analysis
1.5 Objectives and Scope of the Paper
1.6 Structure of the Paper

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Chapter 2: Background and Related Work
2.1 Abstract Interpretation and Abstract Domains
2.2 Timing Analysis in Real-Time Systems
2.3 Expression Abstraction Techniques
2.4 Max Operator in Abstract Interpretation
2.5 Previous Approaches in Numerical Domain Construction
2.6 Challenges in Numerical Timing Analysis

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Chapter 3: Preliminaries
3.1 Basic Concepts of Abstract Interpretation
3.2 Overview of Timing Analysis and Its Challenges
3.3 Numerical Abstract Domains: Definitions and Properties
3.4 Expression Abstraction in Abstract Interpretation
3.5 Introduction to the Max Operator and Its Role

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Chapter 4: The Numerical Abstract Domain
4.1 Designing the Abstract Domain
4.2 Expression Abstraction Methodology
4.3 Integrating the Max Operator into the Domain
4.4 Key Properties of the Abstract Domain
4.5 Advantages over Existing Abstract Domains

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Chapter 5: Application in Timing Analysis
5.1 Timing Analysis Overview and Techniques
5.2 Modeling Timing Behavior with the Abstract Domain
5.3 Handling Time Constraints Using the Max Operator
5.4 Optimizing Timing Analysis for Real-Time Systems
5.5 Case Studies and Practical Examples

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Chapter 6: Algorithmic Details
6.1 Abstract Interpretation Framework
6.2 Fixed-Point Computation in Timing Analysis
6.3 Applying the Max Operator for Precision and Efficiency
6.4 Data Flow Analysis in Timing Analysis
6.5 Algorithm Complexity Analysis

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Chapter 7: Experimental Evaluation
7.1 Evaluation Criteria for Abstract Domains in Timing Analysis
7.2 Benchmarking the Proposed Domain
7.3 Comparison with Other Timing Analysis Methods
7.4 Performance and Accuracy Results
7.5 Case Studies on Real-Time System Verification

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Chapter 8: Practical Implications and Use Cases
8.1 Applications in Embedded Systems
8.2 Real-Time Scheduling and Resource Allocation
8.3 Modeling and Verifying Timing Behavior in Hardware Systems
8.4 Applications in Safety-Critical Systems
8.5 Future Applications in Other Domains

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Chapter 9: Challenges and Future Work
9.1 Scalability Challenges in Timing Analysis
9.2 Handling Complex Time Behavior and Hybrid Systems
9.3 Integrating with Other Formal Verification Techniques
9.4 Extending the Abstract Domain for Broader Use
9.5 Future Directions in Timing Analysis and Abstract Interpretation

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Chapter 10: Conclusion
10.1 Summary of Contributions
10.2 Impact on Timing Analysis in Real-Time Systems
10.3 Key Findings and Observations
10.4 Concluding Remarks on Numerical Abstract Domains and Their Future
10.5 Final Thoughts on Expression Abstraction and Max Operator

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