Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9657817 | Theoretical Computer Science | 2005 | 18 Pages |
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 #·ΠkP,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.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Arnaud Durand, Miki Hermann, Phokion G. Kolaitis,