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than decision problems. One such class, consisting of counting problems, is called : whereas an NP problem asks "Are there any solutions?", the corresponding #P problem asks "How many solutions are there?". Clearly, a #P problem must be at least as hard as the corresponding NP problem, since a count of solutions immediately tells if at least one solution exists, if the count is greater than zero. Surprisingly, some #P problems that are believed to be difficult correspond to easy (for example linear-time) P problems.

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