CoNPvollständig

CoNPvollständig is a complexity class in theoretical computer science. It represents problems for which a proposed solution can be verified in polynomial time, and whose complement is NP-vollständig. In simpler terms, if you are given a potential solution to a coNPvollständig problem, you can quickly check if it is indeed a valid solution. The difficulty arises from the fact that finding such a solution is believed to be hard.

The complement of NP, denoted as coNP, is the class of decision problems for which a "no" answer can be verified in polynomial time. This means if a problem instance has no solution, there exists a short proof that demonstrates this fact. The relationship between NP and coNP is a fundamental question in complexity theory. It is widely believed that NP is not equal to coNP, meaning there are problems in coNP that are not in NP, and vice versa.

A problem is considered coNPvollständig if it is in coNP and every other problem in coNP can be reduced to it in polynomial time. This means that if you could solve any coNPvollständig problem efficiently, you could solve every problem in coNP efficiently. Examples of problems believed to be coNPvollständig include Tautology (determining if a Boolean formula is always true) and Prime Number (determining if a given number is prime, though this has since been shown to be in P). The exact set of coNPvollständig problems is still an active area of research.