Subtractive Reductions and Complete Problems for Counting Complexity Classes

  • Authors:
  • Arnaud Durand;Miki Hermann;Phokion G. Kolaitis

  • Affiliations:
  • -;-;-

  • Venue:
  • MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
  • Year:
  • 2000

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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 #ċΠkP, 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 #ċcoNP) 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.