Theory of linear and integer programming
Theory of linear and integer programming
Acta Informatica
Polynomial-time 1-Turing reductions from #PH to #P
Theoretical Computer Science
On the Complexity of Counting the Hilbert Basis of a Linear Diophnatine System
LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
Reducing the Number of Solutions of NP Functions
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
An algebraic approach to the complexity of generalized conjunctive queries
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
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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.