BQP or PP which are defined symmetrically with regards to their yes and no instances are closed under complement. In contrast, classes such as RP and co-RP define their probabilities with one-sided error, and so are not (currently known to be) closed under complement. Some of the most surprising complexity results shown to date showed that the complexity classes NL and SL are in fact closed under complement, whereas before it was widely believed they were not (see Immerman–Szelepcsényi theorem). The latter has become less surprising now that we know SL equals L, which is a deterministic class. Every class which is low for itself is closed under complement. References Computational complexity theory