Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
The topology of provability in complexity theory
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
Oracles for structural properties: the isomorphism problem and public-key cryptography
Journal of Computer and System Sciences
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
Lattice Embeddings for Abstract Bounded Reducibilities
SIAM Journal on Computing
On the Structure of the Simulation Order of Proof Systems
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
On Diagonalization Methods and the Structure of Language Classes
Proceedings of the 1983 International FCT-Conference on Fundamentals of Computation Theory
On reducibility and symmetry of disjoint NP pairs
Theoretical Computer Science - Mathematical foundations of computer science
SIAM Journal on Computing
Optimal Proof Systems, Optimal Acceptors and Recursive Presentability
Fundamenta Informaticae
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
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
Unions of disjoint NP-complete sets
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
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
Optimal Proof Systems, Optimal Acceptors and Recursive Presentability
Fundamenta Informaticae
the informational content of canonical disjoint NP-pairs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Unions of Disjoint NP-Complete Sets
ACM Transactions on Computation Theory (TOCT)
| Hi-index | 5.23 |
We prove that every disjoint NP-pair is polynomial-time, many-one equivalent to the canonical disjoint NP-pair of some propositional proof system. Therefore, the degree structure of the class of disjoint NP-pairs and of all canonical pairs is identical. We show that this degree structure is not superficial: Assuming there exist P-inseparable disjoint NP-pairs, every countable distributive lattice can be embedded into every interval of polynomial NP-degrees of disjoint pairs by maps that preserve the least and greatest element, respectively. As one consequence of this embedding, under the same assumption, there exist intermediate disjoint NP-pairs. That is, if (A,B) is a P-separable disjoint NP-pair and (C,D) is a P-inseparable disjoint NP-pair, then there exist P-inseparable, incomparable NP-pairs (E,F) and (G,H) whose degrees lie strictly between (A,B) and (C,D). Furthermore, between any two disjoint NP-pairs that are comparable and inequivalent, such a diamond exists.