GapP is a
counting complexity class
In computational complexity theory and computability theory, a counting problem is a type of computational problem. If ''R'' is a search problem then
:c_R(x)=\vert\\vert \,
is the corresponding counting function and
:\#R=\
denotes the corresp ...
, consisting of all of the functions ''f'' such that there exists a polynomial-time
non-deterministic Turing machine
In theoretical computer science, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations. That is, an NTM's next state is ''not'' comp ...
''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