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SIAM Journal on Algebraic and Discrete Methods
Theory of linear and integer programming
Theory of linear and integer programming
Some observations on the connection between counting and recursion
Theoretical Computer Science
Acta Informatica
Polynomial-time 1-Turing reductions from #PH to #P
Theoretical Computer Science
The complexity of model checking for circumscriptive formulae
Information Processing Letters
Descriptive complexity of #P functions
Journal of Computer and System Sciences
On the counting complexity of propositional circumscription
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Complexity of Counting the Optimal Solutions
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Counting Complexity of Minimal Cardinality and Minimal Weight Abduction
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
Fast Counting with Bounded Treewidth
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
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Complexity of Constraints
Complexity of counting the optimal solutions
Theoretical Computer Science
Counting complexity of propositional abduction
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
On the complexity of computing generators of closed sets
ICFCA'08 Proceedings of the 6th international conference on Formal concept analysis
Counting complexity of propositional abduction
Journal of Computer and System Sciences
The complexity of counting functions with easy decision version
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
The Complexity of Reasoning for Fragments of Autoepistemic Logic
ACM Transactions on Computational Logic (TOCL)
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PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
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PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Tractable counting of the answers to conjunctive queries
Journal of Computer and System Sciences
The complexity of weighted counting for acyclic conjunctive queries
Journal of Computer and System Sciences
On the complexity of query result diversification
Proceedings of the VLDB Endowment
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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 # ċ 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 # ċ 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.