In computational complexity theory, a complexity class is a set of problems of related complexity. A typical complexity class has a definition of the form:

the set of problems that can be solved by abstract machine M using O(f(n)) of resource R (n is the size of the input)

For example, the class NP is the set of decision problems that can be solved by a non-deterministic Turing machine in polynomial time, while the class PSPACE is the set of decision problems that can be solved by a deterministic Turing machine in polynomial space . Some complexity classes are sets of function problems, such as FP.

Many complexity classes can be characterized in terms of the mathematical logic needed to express them; see descriptive complexity.

See also: List of complexity classes