A new algorithm for Solving 3-CNF-SAT problem

TL;DR

This paper proposes a novel polynomial-time algorithm for the 3-CNF-SAT problem by reinterpreting clause compatibility, potentially challenging the NP-Complete status of the problem.

Contribution

It introduces a new viewpoint that reduces the problem's complexity from exponential to polynomial by focusing on clause compatibility rather than truth table enumeration.

Findings

The algorithm can determine satisfiability in O(n^{10}) time.

It processes clauses instead of truth table strings, reducing complexity.

The approach offers a polynomial-time solution to a traditionally NP-Complete problem.

Abstract

NP-Complete problems have an important attribute that if one NP-Complete problem can be solved in polynomial time, all NP-Complete problems will have a polynomial solution. The 3-CNF-SAT problem is a NP-Complete problem and the primary method to solve it checks all values of the truth table. This task is of the {\Omega}(2^n) time order. This paper shows that by changing the viewpoint towards the problem, it is possible to know if a 3-CNF-SAT problem is satisfiable in time O(n^10) or not? In this paper, the value of all clauses are considered as false. With this presumption, any of the values inside the truth table can be shown in string form in order to define the set of compatible clauses for each of the strings. So, rather than processing strings, their clauses will be processed implicating that instead of 2^n strings, (O(n^3)) clauses are to be processed; therefore, the time and space complexity of the algorithm would be polynomial.