- 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 counting 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
If NC is a complexity class associated with non-deterministic machines then #C = {#R | R ∈ NC} is the set of counting problems associated with each search problem in NC. In particular, #P is the class of counting problems associated with NP search problems.
- This article incorporates material from counting problem on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
- This article incorporates material from counting complexity class on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
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