Unraveling the P vs NP Problem in Computer Science

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Discussion Overview

The discussion revolves around the P vs NP problem in computer science, exploring whether P is equal to NP and the implications of this question. Participants share their thoughts on the potential for a solution, the nature of P and NP problems, and the challenges faced in proving the conjecture. The conversation includes both theoretical and conceptual aspects of the problem.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants express a belief that P is not equal to NP, with one suggesting that it may be undecidable.
  • There is a discussion about the challenges in proving P vs NP, with questions raised about the complexity of the problem and whether it is comprehensible to those with limited mathematical background.
  • Examples of P and NP problems are provided, such as matrix inversion as a P problem and solving a minesweeper puzzle as an NP problem.
  • One participant suggests that boolean algebra might offer a solution to the problem through logic, while expressing skepticism about the feasibility of statistical formulas in creating AI.
  • Another participant notes that many problems are undecidable, complicating the discussion around specific examples.

Areas of Agreement / Disagreement

Participants generally agree that P is likely not equal to NP, but there is no consensus on the nature of the problem or the possibility of a solution. The discussion remains unresolved with multiple competing views on the topic.

Contextual Notes

Participants express varying levels of understanding and background in computer science, which may affect their interpretations of the P vs NP problem. The complexity of the problem and the undecidability of many related issues are acknowledged but not fully explored.

shamieh
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Didn't know what forum to post this in..There are some brilliant people on this forum, just wanted to know your thoughts on the P vs NP problem in Computer Science? Do you think it will ever be solved? I think P != NP. That being said, I do believe it could be solved but not with normal mathematics. I believe that boolean algebra may be able to solve the problem through LOGIC. As far as statistical formulas creating a Computer AI, I just don't think it's possible. After all, we aren't machines.
 
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Of course $\text{P} \neq \text{NP}$ , but I believe this is more or less undecidable.
 
It seems like it is pretty obvious that P != NP, but how come no one can prove it? Can you give me a example? Like what are the problems people are running into? Or is it too advanced for me to even comprehend? I'm in Calculus II.
 
Most problems are more or less undecidable whether in P or NP, so I can't really give you some nontrivial ones. What background have you got in computer science?
 
shamieh said:
It seems like it is pretty obvious that P != NP, but how come no one can prove it? Can you give me a example? Like what are the problems people are running into? Or is it too advanced for me to even comprehend? I'm in Calculus II.

One example of a P problem is the inversion of a matrix.

One example of an NP problem is to solve a minesweeper puzzle.

P problems are those which have an algorithm to solve them which takes a number of steps that is a polynomial on the input. In the matrix case, the input are the numbers in the matrix.

NP problems are those which don't have an algorithm to solve them which takes a number of steps that is a polynomial on the input. But this special class of problems also has the property that if you could find a polynomial algorithm to solve one of them, you would solve all of them in polynomial time.

The thing is that you haven't still proved that there is no polynomial algorithm to solve an NP problem. That's the P vs NP millenium problem, which is worth $ 1 000 000.
 

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