The P Versus NP Problem

[Pro]

The P Versus NP Problem.

[Pro]

It's pretty much impossible for me to rewrite the protheory.com topics in full as I'd end up just making it too complicated so for now please just take a look at this original archive from my website and then you can ask me any questions below here

P versus NP



Introduction

This problem is about efficiency.

Problems of class P can be solved in a finite amount of time, and problems of class NP require an infinite amount of time to solve.



Questions

It seems to be theoretically possible to create some questions that would take us millions of years to solve using our current technology.



Atom

Imagine trying to calculate the amount of atoms in the universe.



Infinite

Any answer requires an infinite amount of explanations, or at least an infinite amount of time to complete.


Better

We need to know if there is a more efficient way to solve these problems, or if we are stuck with the method of eliminating all steps individually, which could take us an infinite amount of time.



Amount

The amount of possible combinations seems to be so large as to defy any direct attempts to solve the problem using our current technology.



Proven

Nobody has yet proven whether these tasks can actually exist, or whether they are illusory.



Summary

Do questions or tasks exist that could take us an infinite amount of time to solve?

Is there a formula or shortcut that will allow us to solve them in a finite amount of time?



The Millennium Problem

The Millennium problem is to explain the nature of this kind of infinite problem and to prove whether or not they can actually exist.

For the exact problem description please refer to Claymath.org



The Answer



Conjecture

The P versus NP problem presents us with two options, either we can solve these questions in a finite amount of time or we cannot, and asks us to choose one of them.



Dealing

We are dealing with opposite and neutral potentials, regardless of the specific details of each individual question.



Remember

All questions have three simultaneous answers.



Details

All details are relative and subject to change in three ways simultaneously.



Three

We are dealing with three possibilities at all relative times therefore we have three possible types of task or question.

1. Finite.

2. Infinite.

3. Neutral.

Simultaneously.



Possibilities

There is the possibility that each type of task may either exist, not exist, or nothing.



Answers

1. Some tasks require a finite amount of time to complete.

2. Some tasks require an infinite amount of time to complete.

3. Some tasks are neutral.

Simultaneously.



Am I wrong?

I simultaneously oppose, agree with, and neutralise all criticism ad infinitum.

My point is literal.

There is no point creating a theory of everything that doesn't work.

[coe]

You are mistaken. All problems in both P and NP can solved in a finite amount of time. The P vs NP question is not about determining whether problems in NP can be solved in a finite amount of time, but whether they can be solved efficiently.

Please refer to any of the following standard textbooks on complexity theory or automata theory for an accurate definition of the problem you are attempting to resolve:

1) Introduction to the Theory of Computation. Michael Sipser

2) Automata Theory, Languages, and Computation. John Hopcroft, Rajeev Motwani and Jeffrey Ullman

3) Algorithm Design. Jon Kleinberg and Eva Tardos

[Pro]

Originally Posted by coe You are mistaken. All problems in both P and NP can solved in a finite amount of time. The P vs NP question is not about determining whether problems in NP can be solved in a finite amount of time, but whether they can be solved efficiently. Please refer to any of the following standard textbooks on complexity theory or automata theory for an accurate definition of the problem you are attempting to resolve: 1) Introduction to the Theory of Computation. Michael Sipser 2) Automata Theory, Languages, and Computation. John Hopcroft, Rajeev Motwani and Jeffrey Ullman 3) Algorithm Design. Jon Kleinberg and Eva Tardos

Hello and welcome to the forum

I'm sorry my understanding of P versus NP is not perfect, and I thank you for correcting me here. All I'm trying to do is get to the absolute crux of the Millennium Problems, namely trying to find the singular answer the problems ask for and then suggesting three answers in place of one as per Pro theory.

In view of your corrective suggestions here, what I'm trying to say is that in theory we can suggest that these problems can be solved effeciently, cannot be solved efficiently plus neutral.

[Anh Pham]

Every question must has an answer, it can be true, false and simultanously. In simultanous case the answer is true with a No.1 condition and is false with condition No.2, so every problem in NP must has an answer by using a NDM or a "super super...super mechine". So everything here is up to time factor no exactly is up to technology, rite?

In your theory you said it requeries infinite time to solve problems in NP is wrong, it should be " greater finite time". if P=NP then everything is possible to solve, it means your TOE is an existing theory. But what happens if P not equal to NP, I know the answer, but I dont talk in here.