Structural complexity 2
Cook reducibility is faster than Karp reducibility in NP
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Cook versus Karp-Levin: separating completeness notions if NP is not small
Theoretical Computer Science
Resource bounded randomness and weakly complete problems
Theoretical Computer Science
Separating NP-Completeness notions under strong Hypotheses
Journal of Computer and System Sciences
Separation of NP-Completeness Notions
SIAM Journal on Computing
Polynomial reducibilities and upward diagonalizations
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Comparing reductions to NP-complete sets
Information and Computation
Comparing reductions to NP-complete sets
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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
| Hi-index | 0.00 |
We prove that if for some ε 0, NP contains a set that is DTIME(2nε))-bi-immune, then NP contains a set that is 2-Turing complete for NP (hence 3-truth-table complete) but not 1-truth-table complete for NP. Thus this hypothesis implies a strong separation of completeness notions for NP. Lutz and Mayordomo (Theor. Comput. Sci. 164 (1996) 141-163) and Ambos-Spies and Bentzien (J. Comput. Syst. Sci. 61(3) (2000) 335-361) previously obtained the same consequence using strong hypotheses involving resource-bounded measure and/or category theory. Our hypothesis is weaker and involves no assumptions about stochastic properties of NP.