Closure Properties of Classes
Complexity classes have a variety of closure properties; for example, decision classes may be closed under negation, disjunction, conjunction, or even under all Boolean operations. Moreover, they might also be closed under a variety of quantification schemes. P, for instance, is closed under all Boolean operations, and under quantification over polynomially sized domains. However, it is most likely not closed under quantification over exponential sized domains.
Each class X which is not closed under negation has a complement class Co-Y, which consists of the complements of the languages contained in X. Similarly one can define the Boolean closure of a class, and so on; this is however less commonly done.
One possible route to separating two complexity classes is to find some closure property possessed by one and not by the other.
Read more about this topic: Complexity Class
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