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 #·ΠP k, 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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Research partially supported by NSF Grant CCR-9732041.
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© 2000 Springer-Verlag Berlin Heidelberg
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Durand, A., Hermann, M., Kolaitis, P.G. (2000). Subtractive Reductions and Complete Problems for Counting Complexity Classes. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_28
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DOI: https://doi.org/10.1007/3-540-44612-5_28
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