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?

• 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 "X_i" 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