is the class of decision problems whose positive instances have polynomial-length certificates verifiable in polynomial time. Equivalently, it is polynomial time on a nondeterministic computation.
A certificate for a positive instance is a polynomial-length string that makes a polynomial-time verifier accept that instance.
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Strictly speaking, only defined for decision problems: cs.stackexchange.com/questions/9664/is-it-necessary-for-np-problems-to-be-decision-problems/128702#128702