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Feb 22, 2025 · Co-NP Class. Co-NP stands for the complement of NP Class. It means if the answer to a problem in Co-NP is No, then there is proof that can be checked in polynomial time. Features: If a problem X is in NP, then its complement X’ is also in CoNP.

co-NP is a subset of PH, which itself is a subset of PSPACE. An example of a problem that is known to belong to both NP and co-NP (but not known to be in P) is Integer factorization: given positive integers m and n, determine if m has a factor less than n and greater than one.

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The integer factorization problem is in NP and in co-NP (and even in UP and co-UP [23]). If the problem is NP-complete, the polynomial time hierarchy will collapse to its first level (i.e., NP = co-NP).

참고로 P - NP문제는 수학계의 최대 난제인 7대 밀레니엄 문제 중 하나이다. P=NP를 증명하거나, P!=NP를 증명하게 되면, 약 12억의 상금과 튜링상 수상 및 모든 컴퓨터과학 업계를 뒤흔들 수 있다. 튜링머신과 다항시간을 기반으로 P-NP문제를 설명 했으니, 이제 각각이 무엇인지에 대해서 설명해보자. 시간복잡도는 문제를 해결하는데 걸리는 시간과 입력의 함수 관계를 말한다. 즉, 특정 문제가 주어졌고, 그 문제에 n=100이라는 입력이 들어왔을 때, 그 문제를 해결하는데 100*100의 …

Jun 11, 2013 · In summary: NP is concerned with a "yes" answer to some decision problem. Co-NP is concerned with a "no" answer to the same, but complemented, decision problem. Do you mean that you use the same polynomial verifier to answer both questions?

Dec 15, 2016 · Since P is closed under compliment, P=co-P. It should also be clear that co-P is a subset of co-NP because P is contained in NP. Since P = co-P, it follows that P is contained in co-NP.

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