Counting problem (complexity)
In computational complexity theory and computability theory, a counting problem is a type of computational problem. If R is a search problem then
is the corresponding counting function and
denotes the corresponding decision problem.
Note that cR is a search problem while #R is a decision problem, however cR can be C Cook-reduced to #R (for appropriate C) using a binary search (the reason #R is defined the way it is, rather than being the graph of cR, is to make this binary search possible).