NP = coNP

NP is equal to coNP.

Statement

Migrated verbatim from co-nondeterministic-polynomial-time § Co-nondeterministic polynomial-time:

The complement class of NP: a decision problem is in coNP if its complement (swapping “yes” and “no” answers) is in NP. Equivalently, coNP is the class of problems for which a “no” answer can be verified in polynomial time given an appropriate certificate.

Notes

source: folklore: the claim carried no citation on the page it was migrated from, and none was invented.

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

class: free because a containment between complexity classes is proved by any argument at all; the reduction-class axis does not discriminate here, and unstated would wrongly suggest the information is missing.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

  • Definitional (complementation), not a theorem; wants a distinct ‘complement-of’ edge type in the target model.