Quantitative relativizations of complexity classes
SIAM Journal on Computing
The complexity of promise problems with applications to public-key cryptography
Information and Control
Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
Promise problems complete for complexity classes
Information and Computation
The complexity of optimization problems
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
Complexity classes without machines: on complete languages for UP
Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
On polynomial-time bounded truth-table reducibility of NP sets to sparse sets
SIAM Journal on Computing
A uniform approach to define complexity classes
Theoretical Computer Science
On reductions of NP sets to sparse sets
Journal of Computer and System Sciences
A taxonomy of complexity classes of functions
Journal of Computer and System Sciences
Computing Solutions Uniquely Collapses the Polynomial Hierarchy
SIAM Journal on Computing
Cook versus Karp-Levin: separating completeness notions if NP is not small
Theoretical Computer Science
P-selective sets and reducing search to decision vs. self-reducibility
Journal of Computer and System Sciences
Separation of NP-Completeness Notions
SIAM Journal on Computing
On an optimal propositional proof system and the structure of easy subsets of TAUT
Theoretical Computer Science - Complexity and logic
Optimal proof systems imply complete sets for promise classes
Information and Computation
SIAM Journal on Computing
Classes of representable disjoint NP-pairs
Theoretical Computer Science
Optimal Proof Systems, Optimal Acceptors and Recursive Presentability
Fundamenta Informaticae
Nondeterministic functions and the existence of optimal proof systems
Theoretical Computer Science
Optimal Proof Systems, Optimal Acceptors and Recursive Presentability
Fundamenta Informaticae
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Disjoint NP-pairs are pairs (A, B) of nonempty, disjoint sets in NP. We prove that all of the following assertions are equivalent: There is a many-one complete disjoint NP-pair; there is a strongly many-one complete disjoint NP-pair; there is a Turing complete disjoint NP-pair such that all reductions are smart reductions; there is a complete disjoint NP-pair for one-to-one, invertible reductions; the class of all disjoint NP-pairs is uniformly enumerable. Let A, B, C, and D be nonempty sets belonging to NP. A smart reduction between the disjoint NP-pairs (A, B) and (C, D) is a Turing reduction with the additional property that if the input belongs to A ∪ B, then all queries belong to C ∪ D. We prove under the reasonable assumption that UP ∩ co-UP has a P-bi-immune set that there exist disjoint NP-pairs (A, B) and (C, D) such that (A, B) is truth-table reducible to (C, D), but there is no smart reduction between them. This paper contains several additional separations of reductions between disjoint NP-pairs. We exhibit an oracle relative to which DistNP has a truth-table-complete disjoint NP-pair, but has no many-one-complete disjoint NP-pair.