https://github.com/jix/minimal_models_example

https://github.com/jix/minimal_models_example

Last synced: 21 days ago
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• Host: GitHub
• URL: https://github.com/jix/minimal_models_example
• Owner: jix
• License: 0bsd
• Created: 2021-01-04T22:32:29.000Z (almost 4 years ago)
• Default Branch: main
• Last Pushed: 2021-01-04T22:45:06.000Z (almost 4 years ago)
• Last Synced: 2024-05-22T22:33:14.761Z (6 months ago)
• Language: Rust
• Size: 3.91 KB
• Stars: 0
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

• awesome-rust-formalized-reasoning - Minimal models - uses a SAT solver to find minimal partial assignments that are model of a CNF formula. (Unclassified / Libraries)

README

        
# Minimal models

Uses a SAT solver to find minimal partial assignments that are model of a CNF

formula. Supports incremental clause additions. Quick and dirty implementation

to illustrate the technique.

This works by maintaining two SAT solver instances, one for the CNF formula

(the positive solver) and one for its negation (the negative solver). As the

negation of a CNF formula is in DNF, we use the Tseytin transformation to

convert the resulting DNF back into an equisatisfiable CNF with auxiliary

variables.

To find a model we first query the positive solver and obtain a complete

assignment that is a model of our formula (if it exists). If we query the

negative solver using a model (complete or partial) of our formula as

assumptions, the result will be UNSAT. The negative solver will then report a

(not necessarily strict) subset of assumptions that are sufficient for

falsifying the formula of the negative solver (called failed literals).

We can minimize the model by iteratively removing a literal from the assignment

and querying the negative solver. If the result becomes SAT, we know the

removed literal is essential and add it back to the assignment. If the result

remains UNSAT, we can permanently remove that candidate and continue with

another literal not known to be essential until none are left. Each time the

result is UNSAT we can also remove all literals not among the failed literals.

I don't have anything to cite right now, but I'm pretty sure this is a known

technique, very similar ideas are used all over the place as part of algorithms

for MaxSAT, QBF, interpolant generation etc.

## Usage

`cat example.cnf - | cargo run --release`

Then press return to find a minimal model and add a clause blocking the found

model.