A Simple Elementary Proof of P=NP based on the Relational Model of E. F. Codd

TL;DR

This paper presents a simplified proof that P equals NP by reformulating the problem within Codd's relational model, eliminating redundancy, and demonstrating polynomial-time simulation of nondeterministic machines.

Contribution

It introduces a novel relational model approach that simplifies the P versus NP problem and provides an elementary proof of their equality.

Findings

Redundancy in complete configurations is unnecessary and harmful.

Shared trichoices enable polynomial-time simulation of nondeterministic machines.

A polynomial-time periodic machine can be simulated in O((p(n))^4) time.

Abstract

The P versus NP problem is studied under the relational model of E. F. Codd. I found that the term "complete configuration" is unnecessary and harmful in computational complexity theory because of excessive symbol redundancy. For an input, its valid sequences of complete configurations are normalized into a relational model of shared trichoices with no redundancy. To simplify the problem, a polynomial time nondeterministic Turing machine is polynomially reduced to a periodic machine, which only reverses its tape head displacement at the tape ends. By enumerating all the O(p(n)) shared trichoices, a polynomial time p(n) periodic machine is simulated in time O((p(n))^4) under logarithmic cost. A simple elementary proof of P=NP is obtained.