https://github.com/tchaumeny/satisfaction

Investigate phase transitions in k-SAT problems
https://github.com/tchaumeny/satisfaction

2-sat 3-sat computer-science phase-transitions sat-solver satisfiability

Last synced: about 2 months ago
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Investigate phase transitions in k-SAT problems

• Host: GitHub
• URL: https://github.com/tchaumeny/satisfaction
• Owner: tchaumeny
• Created: 2025-01-05T19:27:17.000Z (4 months ago)
• Default Branch: master
• Last Pushed: 2025-01-05T19:54:31.000Z (4 months ago)
• Last Synced: 2025-01-18T21:36:22.076Z (4 months ago)
• Topics: 2-sat, 3-sat, computer-science, phase-transitions, sat-solver, satisfiability
• Language: Rust
• Homepage:
• Size: 87.9 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

• awesome-rust-formalized-reasoning - Satisfaction - investigate phase transitions in k-SAT problems. (Unclassified / Libraries)

README

        
# Satisfaction

#### A Rust tool to investigate [phase transitions](https://en.wikipedia.org/wiki/Phase_transition) in [satisfiability problems](https://en.wikipedia.org/wiki/Boolean_satisfiability_problem).

**Satisfaction** combines a random generator of formulas in conjunctive normal form (*CNF*) with a custom *SAT solver* to generate plots of the share of satisfiable formulas for different values of $\alpha$ (the ratio of *clauses* to *variables*).

> I can't get no satisfaction  

> 'Cause I try and I try and I try and I try  

> — The Rolling Stones

### Examples

```console

satisfaction -k 3 -n 50 -s 1000

```

![3-SAT phase transition](./examples/3-sat-n-50-1000-s-p-p.png)

Here we see the transition, at $\alpha_C \approx 4.3$, for 3-SAT problems with $n = 50$ variables.

```console

satisfaction -k 2 -n 1000 -s 1000 --alpha-start 0 --alpha-end 3 --alpha-steps 30

```

![2-SAT phase transition](./examples/2-sat-n-1000-1000-s-p-p.png)

In the case of 2-SAT, the solver algorithm is efficient and we can investigate sharper transitions like this one with $n = 1000$ variables.

### Help

```console

$ satisfaction --help

Investigate phase transition in k-SAT problems

Usage: satisfaction [OPTIONS]

Options:

  -k, --k                       The number k of literals per clause (e.g. 3 for 3-SAT) [default: 3]

  -n, --n                       The number n of available variables [default: 25]

  -s, --samples           The number of generated samples per point (s.p.p.) [default: 100]

      --alpha-start   Lower bound for values of alpha [default: 0]

      --alpha-end       Upper bound for values of alpha [default: 10]

      --alpha-steps   Number of values for alpha [default: 100]

      --verbose                    Verbosity (when turned on, the computed values are displayed)

  -h, --help                       Print help

  -V, --version                    Print version

```

### Resources

* *Computing Science: Can't Get No Satisfaction*, 

* *Phase transitions and complexity in computer science: an overview of the statistical physics approach to the random satisfiability problem*,