[5] If a class is called C, its complement is conventionally labelled co-C. Notice that this is not the complement of the complexity class itself as a set of problems, which would contain a great deal more problems.
Every deterministic complexity class (DSPACE(f(n)), DTIME(f(n)) for all f(n)) is closed under complement,[8] because one can simply add a last step to the algorithm which reverses the answer.
Similarly, probabilistic classes such as BPP, ZPP, 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).