CSIsat Interpolation for LA EUF 1st edtion by Dirk Beyer, Damien Zufferey, Rupak Majumdar ISBN 3540705437 9783540705437

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Product details:

ISBN 10:       3540705437
ISBN 13: 978-3540705437
Author:     Dirk Beyer, Damien Zufferey, Rupak Majumdar    

We present CSIsat, an interpolating decision procedure for the quantifier-free theory of rational linear arithmetic and equality with uninterpreted function symbols. Our implementation combines the efficiency of linear programming for solving the arithmetic part with the efficiency of a SAT solver to reason about the boolean structure. We evaluate the efficiency of our tool on benchmarks from software verification. Binaries and the source code of CSIsat are publicly available as free software.

CSIsat Interpolation for LA+EUF 1st Table of contents:

Chapter 1: Introduction
1.1 Overview of CSIsat Interpolation
1.2 Introduction to LA+EUF (Linear Arithmetic and Equality Uniqueness Formulas)
1.3 Motivation for CSIsat Interpolation
1.4 Importance and Applications of Interpolation in SAT Solvers
1.5 Objectives and Structure of the Paper

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Chapter 2: Background and Related Work
2.1 Overview of Interpolation in SAT Solvers
2.2 Linear Arithmetic and EUF in SAT Solvers
2.3 Previous Approaches to Interpolation for LA+EUF
2.4 Key Contributions and Limitations of Existing Methods
2.5 Challenges in Interpolation for LA+EUF

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Chapter 3: Preliminaries
3.1 Basics of SAT Solving and Interpolation
3.2 Linear Arithmetic (LA) in SAT
3.3 Equality Uniqueness Formulas (EUF)
3.4 Interpolation Theorem and its Role in SAT Solvers
3.5 CSIsat Overview and Its Role in Interpolation

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Chapter 4: CSIsat Interpolation Methodology
4.1 Introduction to CSIsat Algorithm
4.2 Key Ideas and Principles of CSIsat Interpolation
4.3 Step-by-Step CSIsat Interpolation Process
4.4 Handling LA+EUF within CSIsat Framework
4.5 Improvements over Previous Interpolation Techniques

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Chapter 5: Theoretical Analysis of CSIsat Interpolation
5.1 Correctness of the CSIsat Interpolation Algorithm
5.2 Complexity Analysis
5.3 Soundness and Completeness of CSIsat Interpolation
5.4 Comparison with Other Interpolation Methods in LA+EUF
5.5 Limiting Factors and Trade-offs

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Chapter 6: Implementation of CSIsat Interpolation
6.1 Design and Architecture of the CSIsat Solver
6.2 Integration of LA+EUF with CSIsat
6.3 Algorithmic Details and Optimizations
6.4 Handling Large Scale Problems
6.5 Testing and Debugging of the CSIsat Interpolation Implementation

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Chapter 7: Experimental Evaluation
7.1 Evaluation Criteria for Interpolation Methods
7.2 Benchmarking CSIsat on SAT Instances with LA+EUF
7.3 Comparison with Other State-of-the-Art Methods
7.4 Case Studies: Applications of CSIsat Interpolation
7.5 Performance Analysis and Results

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Chapter 8: Applications of CSIsat Interpolation
8.1 Applications in Satisfiability Modulo Theories (SMT)
8.2 Use of CSIsat Interpolation in Verification Problems
8.3 Application in Automated Theorem Proving
8.4 CSIsat in Model Checking and Software Engineering
8.5 Applications in AI and Machine Learning

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Chapter 9: Challenges and Future Work
9.1 Challenges in Scaling CSIsat Interpolation
9.2 Handling More Complex Theories and Constraints
9.3 Improving Efficiency and Parallelization
9.4 Integration with Other Advanced SAT and SMT Solvers
9.5 Potential Directions for Future Research

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Chapter 10: Conclusion
10.1 Summary of Contributions
10.2 Impact of CSIsat Interpolation on SAT Solvers
10.3 Concluding Thoughts on LA+EUF and Interpolation Techniques
10.4 Future Prospects and Open Questions

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