Result: Time‑Step Ratio Theory: A Practical Framework Supporting P ≠ NP Using Two Core Run-Step Conditions

Title:
Time‑Step Ratio Theory: A Practical Framework Supporting P ≠ NP Using Two Core Run-Step Conditions
Authors:
ochimana, Israel ochimana
Publisher Information:
Zenodo
Publication Year:
2025
Collection:
Zenodo
Subject Terms:
P vs NP, computational complexity, theoretical computer science, logic, algorithm analysis
Document Type:
Report report
Language:
English
Relation:
https://zenodo.org/records/16442578; oai:zenodo.org:16442578; https://doi.org/10.5281/zenodo.16442578
DOI:
10.5281/zenodo.16442578
Availability:
https://doi.org/10.5281/zenodo.16442578
https://zenodo.org/records/16442578
Rights:
Creative Commons Attribution 4.0 International ; cc-by-4.0 ; https://creativecommons.org/licenses/by/4.0/legalcode
Accession Number:
edsbas.B5454A2D
Database:
BASE

Further Information

This preprint introduces the Time‑Step Ratio Theory, a practical and intuitive framework designed to support the distinction between P and NP. The theory compares the average step counts required for solving versus checking solutions to logical problems, proposing the inequality Tsolve/Ssolve > Tcheck/Scheck for valid problem-solving cases, and Tsolve/Ssolve ≤ Tcheck/Scheck for edge-case guessing. The framework has been tested on problems from AI, quantum computing, games, and NP-complete scenarios, and aims to provide a new perspective on computational complexity.