Suppose that $K$ is a knot in the three-sphere. Then deciding if $K$ is the unknot lies in NP and also in co-NP. Its containment in NP is due to Hasset al , Lagarias, and Pippenger and the containment in co-NP has been shown (but not yet written up?) by Agol.
Suppose that $K$ is a knot in the three-sphere. Then deciding if $K$ is the unknot lies in NP and also in co-NP. Its containment in NP is due to Hass et al and the containment in co-NP has been shown (but not yet written up?) by Agol.