Subtractive Reductions and Complete Problems for Counting Complexity Classes

Abstract : We introduce and investigate a new type of reductions between counting problems, which we call subtractive reductions. We show that the main counting complexity classes #P, #NP, as well as all higher counting complexity classes #.Pi_k P, k > 2, are closed under subtractive reductions. We then pursue problems that are complete for these classes via subtractive reductions. We focus on the class #NP (which is the same as the class #.coNP) and show that it contains natural complete problems via subtractive reductions, such as the problem of counting the minimal models of a Boolean formula in conjunctive normal form and the problem of counting the cardinality of the set of minimal solutions of a homogeneous system of linear Diophantine inequalities.
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Submitted on : Tuesday, September 26, 2006 - 8:53:27 AM
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Arnaud Durand, Miki Hermann, Phokion G. Kolaitis. Subtractive Reductions and Complete Problems for Counting Complexity Classes. 25th International Symposium on Mathematical Foundations of Computer Science - MFCS'2000, 2000, Bratislava, Slovaquie, pp.323-332. ⟨inria-00099381⟩

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