Questions tagged [p-vs-np]
280 questions
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If a problem is in P solved via dynamic programming, is it also in NP?
So I can solve a given problem using dynamic programming in $O(n^2k^2)$ time complexity. This means that the problem is in P. But I am asked if it is in NP.
My answer is, "Since it is also polynomial time solvable, the problem is also in $NP$".
Is…
unsure_automata
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Why is this a flawed counterexample to P=NP?
I apologize in advance for asking this, since I'm sure this site is flooded by amateurs like me asking about P and NP. If there's a better platform to ask this on, please let me know, but this question has always bothered me.
Suppose you have a…
TimD1
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Is reduction symmetric?
I was watch this lecture https://youtu.be/moPtwq_cVH8?t=2895, and at this point he says a lot about reductions, take a problem and reduce to another problem. From what I could understand this is a symmetric relation, if I can reduce A to B, then I…
geckos
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Are there infinite possibilities to the outcome of the P vs. NP question?
The P vs. NP poll provides 3 possibilities: equal, not equal, and independent. This is reasonable, because despite the law of the excluded middle you must supply a proof for your answer, which itself is insufficient. But then the statement "P vs. NP…
Zirui Wang
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Independence Implies P $\ne$ NP
Suppose P vs. NP is independent of ZFC. Then there cannot be an efficient SAT solver, otherwise it would constitute a proof for P = NP. Therefore P $\ne$ NP.
What we see here is that independence implies unequality. So why is independence a big…
Zirui Wang
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Is this line from the rational wiki p vs np bit correct? " A computational problem is considered "in P
http://rationalwiki.org/wiki/Pseudomathematics#P_vs._NP_problem
A computational problem is considered "in P" if an algorithm exists
that can solve the problem in "polynomial time" — that is, it's O(n),
or O(n2), or O(n3), or any order where the…
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Place 4 notorious problems into 2 diagrams (one assuming P=NP, and the other one assuming P!=NP)
This diagram is on Wikipedia:
On left side we see NP-hard intersecting NP class (assuming P!=NP), on right side we see NP-hard including NP (assuming P=NP)
Where should I place the following problems (assume decisional part)?
Traveling…
CoffeDeveloper
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P = NP: Doesn't a search generate more information than a check?
I feel like I am understanding P ≠ NP fairly well, but there is one issue I feel like I am missing. It seems like a search for an answer generates information that a check does not.
Is this a correct way of looking at it, and if so, how does that…
Tim Brown
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Can we detect perfect matchings in P? in NP? in coNP?
This question concerns the classes P and N P . If you are familiar with them, you may skip the definitions and go directly to the question.
Let L be a set. We say that L is in P if there is some algorithm which given input x decides if x is in L or…
CHETAN RAJPUT
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Are all the NP-complete problems have strong reductions?
Are all the NP-complete problems have strong reductions? If I find a polynomial solution to one NP-complete problem, can I state that P = NP?
Ilya Gazman
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Review my proof that Co-NP != P
The idea is to pick a problem category in Co-NP, where the correct answer is hard to verify because of circuit complexity, express it as 1-in-k SAT formula, and show there also exists a short certificate, whose length in bits is exactly twice the…
user102180