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Counting problem (complexity)

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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).

Counting complexity class[edit]

Just as NP has NP-complete problems via many-one reductions, #P has #P-complete problems via parsimonious reductions, problem transformations that preserve the number of solutions.[1]

See also[edit]


  1. ^ Barak, Boaz (Spring 2006). "Complexity of counting" (PDF). Princeton University.

External links[edit]