Papers
Topics
Authors
Recent
Detailed Answer
Quick Answer
Concise responses based on abstracts only
Detailed Answer
Well-researched responses based on abstracts and relevant paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses
Gemini 2.5 Flash
Gemini 2.5 Flash 60 tok/s
Gemini 2.5 Pro 51 tok/s Pro
GPT-5 Medium 18 tok/s Pro
GPT-5 High 14 tok/s Pro
GPT-4o 77 tok/s Pro
Kimi K2 159 tok/s Pro
GPT OSS 120B 456 tok/s Pro
Claude Sonnet 4 38 tok/s Pro
2000 character limit reached

Simulating Polynomial-Time Nondeterministic Turing Machines via Nondeterministic Turing Machines (2406.10476v20)

Published 15 Jun 2024 in cs.CC

Abstract: We prove in this paper that there is a language $L_s$ accepted by some nondeterministic Turing machine that runs within time $O(nk)$ for any positive integer $k\in\mathbb{N}_1$ but not by any ${\rm co}\mathcal{NP}$ machines. Then we further show that $L_s$ is in $\mathcal{NP}$, thus proving that $\mathcal{NP}\neq{\rm co}\mathcal{NP}$. The main techniques used in this paper are simulation and the novel new techniques developed in the author's recent work. Our main result has profound implications, such as $\mathcal{P}\neq\mathcal{NP}$, etc. Further, if there exists some oracle $A$ such that $\mathcal{P}A\ne\mathcal{NP}A={\rm co}\mathcal{NP}A$, we then explore what mystery lies behind it and show that if $\mathcal{P}A\ne\mathcal{NP}A={\rm co}\mathcal{NP}A$ and under some rational assumptions, then the set of all ${\rm co}\mathcal{NP}A$ machines is not enumerable, thus showing that the simulation techniques are not applicable for the first half of the whole step to separate $\mathcal{NP}A$ from ${\rm co}\mathcal{NP}A$. Finally, a lower bounds result for Frege proof systems is presented (i.e., no Frege proof systems can be polynomially bounded).

Summary

We haven't generated a summary for this paper yet.

List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

Lightbulb On Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (1)

X Twitter Logo Streamline Icon: https://streamlinehq.com