GapP is a counting complexity class, consisting of all of the functions ''f'' such that there exists a polynomial-time non-deterministic Turing machine ''M'' where, for any input ''x'', ''f(x)'' is equal to the number of accepting paths of ''M'' minus the number of rejecting paths of ''M''. GapP is exactly the closure of #P under subtraction. It also has all the other closure properties of #P, such as addition, multiplication, and binomial coefficients. The counting class AWPP is defined in terms of GapP functions.

References

* S. Fenner, L. Fortnow, and S. Kurtz
Gap-definable counting classes
''Journal of Computer and System Sciences'' 48(1):116-148, 1994. * {{Comp-sci-theory-stub Complexity classes