A Real World Mechanism for Testing Satisfiability in Polynomial Time

TL;DR

This paper proposes a novel physical mechanism using light and electrochemical properties to test the satisfiability of propositional formulas in CNF form in linear time, suggesting a potential breakthrough in computational complexity.

Contribution

It introduces a real-world, physical device capable of determining CNF satisfiability in linear time, challenging traditional computational limitations.

Findings

Blueprint for a machine testing CNF satisfiability in linear time

Uses light and electrochemical properties for computation

Device adapts to problem scope without exponential growth

Abstract

Whether the satisfiability of any formula F of propositional calculus can be determined in polynomial time is an open question. I propose a simple procedure based on some real world mechanisms to tackle this problem. The main result is the blueprint for a machine which is able to test any formula in conjunctive normal form (CNF) for satisfiability in linear time. The device uses light and some electrochemical properties to function. It adapts itself to the scope of the problem without growing exponentially in mass with the size of the formula. It requires infinite precision in its components instead.