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https://github.com/snsinfu/dpll-sat
Naïve SAT solver implementing the classic DPLL algorithm
https://github.com/snsinfu/dpll-sat
dpll-algorithm learning sat-solver
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Naïve SAT solver implementing the classic DPLL algorithm
- Host: GitHub
- URL: https://github.com/snsinfu/dpll-sat
- Owner: snsinfu
- License: mit
- Created: 2021-04-08T16:53:39.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2021-04-13T16:03:11.000Z (over 3 years ago)
- Last Synced: 2024-05-22T19:32:00.611Z (6 months ago)
- Topics: dpll-algorithm, learning, sat-solver
- Language: Rust
- Homepage:
- Size: 536 KB
- Stars: 1
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE.txt
Awesome Lists containing this project
- awesome-rust-formalized-reasoning - dpll-sat - naïve SAT solver implementing the classic DPLL algorithm. (Projects / Provers and Solvers)
README
# dpll-sat
[![Build Status][build-badge]][build-url]
[build-badge]: https://github.com/snsinfu/dpll-sat/workflows/test/badge.svg
[build-url]: https://github.com/snsinfu/dpll-sat/actions?query=workflow%3Atest
**dpll-sat** is a SAT solver implementing the classic [DPLL algorithm][dpll]. I
wrote this program for learning purposes and also for comparing the performance
of a naive DPLL solver and modern solvers.
- [Build](#build)
- [Usage](#usage)
- [Implementation notes](#implementation-notes)
- [Benchmarks](#benchmarks)
- [References](#references)
[dpll]: https://en.wikipedia.org/wiki/DPLL_algorithm
## Build
```console
$ git clone https://github.com/snsinfu/dpll-sat
$ cd dpll-sat
$ cargo build --release
$ cp target/release/dpll-sat ~/bin/
```
## Usage
**dpll-sat** command reads [a simplified DIMACS CNF][format] from stdin. It
prints "sat" followed by an assignment and exits with exit code 0 if the formula
is satisfiable. Otherwise, it prints "unsat" and exits with exit code 1.
```console
$ dpll-sat < examples/qg3-08.cnf
sat
1 2 3 4 5 6 7 8 -9 -10 -11 -12 -13 -14 -15 -16 -17 ...
```
The second line shows an assignment. A positive number `i` means that the i-th
variable is true. A negative number `-i` means that the i-th variable is false.
The output format is essentially the same as that of [z3][z3].
[format]: http://www.satcompetition.org/2011/format-benchmarks2011.html
[z3]: https://github.com/Z3Prover/z3
## Implementation notes
The algorithm is implemented in the following way in pseudocode:
```javascript
function DPLL(formula, vars) {
// Simplify formula by determining variables in unit clauses.
formula = copy(formula);
unit_propagate(formula, vars);
// Stopping conditions.
if (formula is empty) {
return "SAT";
}
if (empty clause in formula) {
return "UNSAT";
}
// Choose a branching literal and recurse.
v = choose_literal(formula);
return DPLL(formula + [v], vars) || DPLL(formula + [not(v)], vars);
}
```
- Pure literal elimination is not implemented due to the complexity of keeping
track of the polarity of every literal in a formula.
- The branching literal is chosen to be the most-used variable in a formula.
The literal is eliminated in the next recursion, so this strategy eagerly
reduces the size of the formula.
- Every recursion creates a new copy of a formula. This is inefficient. The copy
is necessary because the algorithm eliminates some clauses and literals in a
formula and later revert it for backtracking. But, most clauses are untouched.
There would be a clever data structure that can reduce the number of copies.
Maybe deque?
- A formula is represented as a vector-of-vectors. It's horribly inefficient
since a formula tends to consist of many small clauses, making memory access
extremely scattered. It would be much better to use a flat vector with
sentinel values.
## Benchmarks
Run time for some benchmark instances found on [the satlib site][satlib] and a
[benchmark page][bench]. The run time is the total "USER" time spent from a
program startup to termination. Benchmarks ran on Fedora 33 Linux with AMD Ryzen
3600 CPU @ 4.2GHz (boost).
| Instance | #var | #clause | dpll | z3 | cadical |
|-------------------------------------------|------|---------|--------|--------|---------|
| Random 3-SAT CBS_k3_n100_m403_b10_0.cnf | 100 | 403 | 0.03s | 0.01s | 0.00s |
| blocksworld huge.cnf | 459 | 7054 | 0.15s | 0.00s | 0.00s |
| SAT-02 glassy-sat-sel_N210_n.shuffled.cnf | 210 | 980 | 215min | 0.85s | 0.31s |
| SAT-02 homer10.shuffled.cnf | 360 | 3460 | > 1day | 12.77s | 4.22s |
Z3 does pretty good job considering [CaDiCaL][cadical] is the top-1 winner in
the SAT track of the SAT Race 2019.
[satlib]: https://www.cs.ubc.ca/~hoos/SATLIB/
[bench]: https://www.cs.ubc.ca/~hoos/SATLIB/benchm.html
[cadical]: http://fmv.jku.at/cadical/
## References
This lecture note is useful to understand the DPLL algorithm:
- http://www.cs.cornell.edu/courses/cs4860/2009sp/lec-04.pdf
This book has a ton of examples:
- https://sat-smt.codes/