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Counting problem (complexity)
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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).
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.
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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).
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.