3-SAT Polynomial Solution of Knowledge Recognition Algorithm

TL;DR

This paper presents a polynomial-time knowledge recognition algorithm (KRA) for solving the 3SAT problem by iterative set relation recognition, avoiding direct search of variable assignments.

Contribution

It introduces a novel approach applying Chinese COVA* principles and eliminating OR operations to recognize satisfiability without exhaustive search.

Findings

KRA can determine 3SAT satisfiability in polynomial time.

The algorithm recognizes unsatisfiable clauses through iterative rejection.

Multiple solutions are identified when more than one clause remains.

Abstract

This paper introduces a knowledge recognition algorithm (KRA) for solving the 3SAT problem in polynomial time. KRA learns member-class relations and retrieves information through deductive and reductive iterative reasoning. It applies the principle of Chinese COVA* (equivalent to a set of eight 3-variable conjunctive clauses) and eliminates the "OR" operation to solve 3-SAT problem. That is, KRA does not search the assignment directly. It recognizes the complements as rejections at each level of the set through iterative set relation recognition. KRA recognizes which conjunctive 3-variable-clause is not satisfiable. If all the eight clauses of any set of 3-variable clauses are rejected, then there is not an assignment for the formula. If there is at least one clause in each set that remains, then there is at least one assignment that is the union of clauses of each set. If there is more than one clause in each set that remains, then there are multiple assignments that are the unions of the clauses of each set respectively.