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On the parameterized complexity of approximate counting. (English) Zbl 1234.68121
Summary: We study the parameterized complexity of approximating the parameterized counting problems contained in the class #\(W[P]\), the parameterized analogue of #\(P\). We prove a parameterized analogue of a famous theorem of Stockmeyer claiming that approximate counting belongs to the second level of the polynomial hierarchy.

68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
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