Reductions between disjoint NP-pairs
Information and Computation
Canonical disjoint NP-pairs of propositional proof systems
Theoretical Computer Science
Classes of representable disjoint NP-pairs
Theoretical Computer Science
The Shrinking Property for NP and coNP
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Nondeterministic functions and the existence of optimal proof systems
Theoretical Computer Science
Characterizing the Existence of Optimal Proof Systems and Complete Sets for Promise Classes
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Reductions between disjoint NP-Pairs
Information and Computation
The deduction theorem for strong propositional proof systems
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Proof system representations of degrees of disjoint NP-pairs
Information Processing Letters
The shrinking property for NP and coNP
Theoretical Computer Science
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Disjoint NP-pairs from propositional proof systems
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Canonical disjoint NP-Pairs of propositional proof systems
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Survey of disjoint NP-pairs and relations to propositional proof systems
Theoretical Computer Science
A thirty year old conjecture about promise problems
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
the informational content of canonical disjoint NP-pairs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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We study the question of whether the class DisjNP of disjoint pairs (A, B) of NP-sets contains a complete pair. The question relates to the question of whether optimal proof systems exist, and we relate it to the previously studied question of whether there exists a disjoint pair of NP-sets that is NP-hard. We show under reasonable hypotheses that nonsymmetric disjoint NP-pairs exist, which provides additional evidence for the existence of P-inseparable disjoint NP-pairs. We construct an oracle relative to which the class of disjoint NP-pairs does not have a complete pair; an oracle relative to which optimal proof systems exist, and hence complete pairs exist, but no pair is NP-hard; and an oracle relative to which complete pairs exist, but optimal proof systems do not exist.