Inferring Congruence Equations Using SAT 1st edition by Andy King, Harald Sondergaard ISBN 3540705437 9783540705437

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Product details:

ISBN 10:       3540705437
ISBN 13: 978-3540705437
Author:         Andy King, Harald Søndergaard

This paper proposes a new approach for deriving invariants that are systems of congruence equations where the modulo is a power of 2. The technique is an amalgam of SAT-solving, where a propositional formula is used to encode the semantics of a basic block, and abstraction, where the solutions to the formula are systematically combined and summarised as a system of congruence equations. The resulting technique is more precise than existing congruence analyses since a single optimal transfer function is derived for a basic block as a whole.

Inferring Congruence Equations Using SAT 1st Table of contents:

Chapter 1: Introduction
1.1 Overview of Congruence Equations
1.2 Significance of Congruence Equations in Formal Verification
1.3 Introduction to SAT (Satisfiability Problem)
1.4 Motivation for Using SAT to Infer Congruence Equations
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 Congruence Equations: Definitions and Applications
2.2 The Role of SAT in Logic and Verification
2.3 Previous Approaches to Inferring Congruence Equations
2.4 Use of SAT Solvers in Formal Methods and Verification
2.5 Challenges in Inferring Congruence Equations Using SAT

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Chapter 3: Theoretical Foundation
3.1 Mathematical Foundations of Congruence Equations
3.2 SAT Problem Overview and Satisfiability
3.3 Reduction of Congruence Equations to SAT Problems
3.4 Types of Congruence Equations in Verification
3.5 Formalizing Congruence Equation Inference Using SAT

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Chapter 4: SAT Solvers and Their Role in Inference
4.1 Introduction to Modern SAT Solvers
4.2 SAT Solver Architecture and Techniques
4.3 Encoding Congruence Equations into SAT
4.4 Solving Congruence Equations with SAT Solvers
4.5 Comparative Analysis of SAT Solvers for Congruence Inference

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Chapter 5: Algorithmic Approach for Inferring Congruence Equations
5.1 Algorithm Overview for Inferring Congruence Equations Using SAT
5.2 Encoding Variables and Constraints into SAT
5.3 Optimization Techniques for SAT-Based Inference
5.4 Handling Large and Complex Congruence Systems
5.5 Algorithmic Complexity and Efficiency Analysis

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Chapter 6: Case Studies and Applications
6.1 Case Study 1: Congruence Inference in Cryptographic Systems
6.2 Application in Software Verification
6.3 Application in Hardware Design and Verification
6.4 Real-World Examples of Congruence Equation Inference Using SAT
6.5 Lessons Learned from Case Studies

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Chapter 7: Experimental Evaluation
7.1 Experimental Setup and Methodology
7.2 Benchmarking SAT Solvers for Congruence Inference
7.3 Comparison of Performance in Different Domains
7.4 Evaluating the Efficiency of the Proposed Approach
7.5 Results and Analysis

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Chapter 8: Challenges and Limitations
8.1 Scalability of SAT-Based Congruence Equation Inference
8.2 Dealing with Intractable Congruence Systems
8.3 Limitations in SAT Encoding for Congruence Equations
8.4 Accuracy and Completeness of Inferred Equations
8.5 Challenges in Automated Verification and Real-World Applications

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Chapter 9: Future Directions and Open Problems
9.1 Improving Efficiency in SAT-Based Congruence Inference
9.2 Exploring Alternative Encoding Techniques
9.3 Integration with Other Formal Methods and Tools
9.4 Future Research Directions in Congruence Equation Inference
9.5 Long-Term Impact on Formal Verification Methods

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Chapter 10: Conclusion
10.1 Summary of Key Contributions
10.2 Impact of SAT on Congruence Equation Inference
10.3 Final Remarks on the Future of SAT-Based Formal Methods
10.4 Concluding Thoughts on Congruence Equations and SAT Solvers

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