https://github.com/curtisfenner/cnf-solver

A small CNF-SAT solver implementing simple conflict driven clause learning (CDCL) and a simple branching heuristic.
https://github.com/curtisfenner/cnf-solver

cnf sat-solver

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A small CNF-SAT solver implementing simple conflict driven clause learning (CDCL) and a simple branching heuristic.

• Host: GitHub
• URL: https://github.com/curtisfenner/cnf-solver
• Owner: CurtisFenner
• License: lgpl-3.0
• Created: 2018-07-23T17:16:58.000Z (almost 8 years ago)
• Default Branch: master
• Last Pushed: 2018-09-14T03:02:55.000Z (over 7 years ago)
• Last Synced: 2025-03-24T00:15:59.429Z (about 1 year ago)
• Topics: cnf, sat-solver
• Language: Lua
• Homepage:
• Size: 24.4 KB
• Stars: 2
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: readme.md
  • License: LICENSE.txt

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README

          
# cnf-solver, a simple CNF-SAT solver

The CNF-SAT problem is a well-known and well-studied NP-complete problem. This

means computer scientists and mathematicians believe there is no algorithm that

is guaranteed to terminate in polynomial time (or even in sub-exponential time).

Despite this theoretical limitation, many approaches have been found to solve

many instances of the CNF-SAT problem very quickly. Two early methods have

proven extremely effective:

* Unit propagation (aka boolean constraint propagation):

    force an assignment whenever a clause has only one remaining literal

* Conflict Driven Clause Learning (CDCL):

    add additional clauses to prune the search space further

cnf-solver implements these in Lua with thorough documentation. Lua was chosen

because it is simple, readable, and portable. These features make this

cnf-solver very easy to run and learn from.

## Getting started

These instructions explain how to use the scripts provided to solve (small) CNF

instances.

### Prerequisites

You need a version of [Lua](https://lua.org) to run the CNF solver. You may

already have Lua installed on your system; try `lua -v` to see the version.

This project is compatible with Lua versions 5.1, 5.2, and 5.3, in addition to

LuaJIT. LuaJIT runs the solver 2x-3x faster than the standard Lua interpreter.

### Solving DIMACS .cnf files

The `run_dimacs.lua` script can read simple DIMACS-style .cnf files. Check out

[the example inputs](input) for what this format looks like.

    $ lua run_dimacs.lua < input/too_hard.cnf

    SAT:    true

            x7      =>      true

            x6      =>      false

            x5      =>      false

            x4      =>      true

            x2      =>      true

            x3      =>      true

            x1      =>      false

            x8      =>      false

            x9      =>      false

## Using the ClauseDatabase library

Require the Lua library as usual. A CNF formula is created by calling the

`CNF.new()` constructor.

    local CNF = require "clausedatabase"

    local formula = CNF.new()

Add clauses to the formula by invoking `:addClause`. Clauses are passed as lists

of *literals*, where each literal is a `{term, truth}` pair. For example,

"(not a) or b" can be encoded as

    formula:addClause {{"a", false}, {"b", true}}

Ask the formula for a satisfying assignment by invoking `:isSatisfiable()`:

    local model = formula:isSatisfiable()

    if model then

        -- The formula is satisfiable!

        print("Satisfiable:")

        for key, assignment in pairs(model) do

            print(key, "=>", assignment)

        end

    else

        -- The formula is NOT satisfiable (every possible assignment results in

        -- at least one clause being unsatisfied)

        print("Unsatisfiable")

    end

## License

This project is licensed under the LGPL-3.0 license. See

[LICENSE.txt](LICENSE.txt) for details.