https://github.com/sleekpanther/3-sat-certifier

A Certifier algorithm to check a particular solution to the NP-Complete 3-Sat problem
https://github.com/sleekpanther/3-sat-certifier

3-sat 3-satisfiability 3sat certificate certifier-algorithm circuit-satisfiability clause cnf compound-boolean computational-instability conjunctive-normal-form exp literals negation np np-complete np-hard p sat satisfiability

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A Certifier algorithm to check a particular solution to the NP-Complete 3-Sat problem

• Host: GitHub
• URL: https://github.com/sleekpanther/3-sat-certifier
• Owner: SleekPanther
• Created: 2017-04-30T16:29:40.000Z (about 8 years ago)
• Default Branch: master
• Last Pushed: 2017-05-18T22:39:39.000Z (almost 8 years ago)
• Last Synced: 2025-01-15T13:08:07.079Z (4 months ago)
• Topics: 3-sat, 3-satisfiability, 3sat, certificate, certifier-algorithm, circuit-satisfiability, clause, cnf, compound-boolean, computational-instability, conjunctive-normal-form, exp, literals, negation, np, np-complete, np-hard, p, sat, satisfiability
• Language: Java
• Homepage:
• Size: 16.6 KB
• Stars: 1
• Watchers: 2
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# 3-SAT Certifier (3 Satisfiability Problem)

A certifier algorithm for the NP-Complete 3-Satisfiability Problem

## Problem Statement

**Given a Conjunctive Normal Form formula, is there a satisfying truth assignment so that it evaluates to true?**  

![](images/cnf.png)  

- Each clause must have the same number of literals (literals are X1, X2, X3, etc.)  

This is the 3-SAT problem so each clause has **exactly 3 literals**  

**But the code is generic enough to work on ANY NUMBER OF LITERALS in a clause (given that each clause has the same number)**

- The literals in a clauses can have their value flipped using **NOT, boolean negation**

- In each clause, literals (or their negation) are combined with **compound boolean OR**

- All clauses are combined with **compound boolean AND**

- The final result of the CNF is either `1` or `0` (`true` or `false`)

- **The 3-SAT problem asks if this result for all clauses is `true`**

## Certifier Algorithm

This 3-SAT problem is NP-Complete, this not a solution to the problem

**Instead, given a certificate of truth assignments, does the CNF evaluate to true?**  

## Code Details

- Literals must be **"Xi" where i is an integer** 

- Input for the CNF formula is a String with **"AND"** and **"OR"** spelled out

- String parsing is **case-INsensitive**

- Input for certificates a `String` array. Each one in the form:

  - `(x1=1, x2=1, x3=0, x4=1)`

## Sample Certificates

The program parses the following strings to check if they're valid certificates to the CNF  

`(NOT x1 OR X2 OR x3) AND (x1 OR NOT x2 OR x3) AND (x1 OR x2 OR x4) AND (NOT x1 OR NOT x3 OR NOT x4)`

1. `(x1=1, x2=1, x3=0, x4=1)` **valid**

2. `(x1=1, x2=1, x3=1, x4=1)` **INVALID**

3. `(x1=0, x2=0, x3=0, x4=1)` **valid**

4. `(x1=0, x2=1, x3=0, x4=1)` **INVALID**