## Table: Analysis Methods Coverage Across Systems
### Overview
The table compares the coverage of various analysis methods across six systems: HOL4, HOL light, Isabelle/HOL, Coq, PVS, and Keymaera. Each cell indicates whether a specific analysis method is supported (✓) or not.
### Components/Axes
- **Rows (Analysis Methods)**:
1. Analysis/Theorem Provers
2. Transform Methods
3. Probabilistic Analysis
4. Performance Analysis
5. Dependability Analysis
6. Hybrid Systems
7. Optical Systems
8. Quantum Systems
9. Robotic Systems
10. Software Components
- **Columns (Systems)**:
1. HOL4
2. HOL light
3. Isabelle/HOL
4. Coq
5. PVS
6. Keymaera
### Detailed Analysis
| Analysis Method | HOL4 | HOL light | Isabelle/HOL | Coq | PVS | Keymaera |
|-------------------------------|------|-----------|--------------|-----|-----|----------|
| **Analysis/Theorem Provers** | ✓ | ✓ | ✓ | ✓ | | |
| **Transform Methods** | ✓ | ✓ | ✓ | | | |
| **Probabilistic Analysis** | ✓ | | ✓ | | | |
| **Performance Analysis** | ✓ | | ✓ | | | |
| **Dependability Analysis** | ✓ | | | | | |
| **Hybrid Systems** | | | | | | ✓ |
| **Optical Systems** | | ✓ | | | | |
| **Quantum Systems** | | ✓ | ✓ | ✓ | | |
| **Robotic Systems** | ✓ | ✓ | ✓ | | ✓ | ✓ |
| **Software Components** | ✓ | ✓ | ✓ | | ✓ | ✓ |
### Key Observations
1. **HOL4** and **Isabelle/HOL** show the broadest coverage, supporting all analysis methods except Hybrid Systems.
2. **HOL light** supports Analysis/Theorem Provers, Transform Methods, Optical Systems, and Quantum Systems.
3. **Coq** is limited to Analysis/Theorem Provers and Quantum Systems.
4. **PVS** and **Keymaera** have sparse coverage:
- PVS supports only Software Components.
- Keymaera supports Hybrid Systems, Robotic Systems, and Software Components.
5. **Robotic Systems** are the most universally supported, with checkmarks in all systems except Coq.
### Interpretation
- **HOL4** and **Isabelle/HOL** are the most versatile tools, covering foundational analysis methods (e.g., Transform Methods, Performance Analysis) and specialized domains like Robotic Systems.
- **Keymaera** and **PVS** appear niche, focusing on Hybrid Systems and Software Components, respectively.
- **Coq** has minimal coverage, suggesting limited use in probabilistic or dependability analysis.
- **Robotic Systems** are the most universally supported, indicating their critical role in multi-tool ecosystems.
- **Hybrid Systems** and **Optical Systems** are underrepresented, with only Keymaera and HOL light, respectively, supporting them.
This table highlights disparities in toolchain maturity, with HOL4 and Isabelle/HOL dominating general-purpose analysis, while specialized systems like Keymaera and PVS target narrower applications.
