The polynomial-time hierarchy and sparse oracles
Journal of the ACM (JACM)
Complexity classes without machines: on complete languages for UP
Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
On hiding information form an oracle
Journal of Computer and System Sciences
Theoretical Computer Science
Strong and robustly strong polynomial-time reducibilities to sparse sets
Theoretical Computer Science
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Counting classes are at least as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Theoretical Computer Science
Algebraic methods for interactive proof systems
Journal of the ACM (JACM)
Oracles and queries that are sufficient for exact learning (extended abstract)
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
Reductions to sets of low information content
Complexity theory
More on BPP and the polynomial-time hierarchy
Information Processing Letters
Computing Solutions Uniquely Collapses the Polynomial Hierarchy
SIAM Journal on Computing
New Collapse Consequences of NP Having Small Circuits
SIAM Journal on Computing
Symmetric alternation captures BPP
Computational Complexity
The complexity theory companion
The complexity theory companion
Recent Directions in Algorithmic Research
Proceedings of the 5th GI-Conference on Theoretical Computer Science
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
On the structure of low sets [complexity classes]
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On some central problems in computational complexity.
On some central problems in computational complexity.
Competing provers yield improved Karp-Lipton collapse results
Information and Computation
Polylogarithmic-round interactive proofs for coNP collapse the exponential hierarchy
Theoretical Computer Science
Competing provers yield improved Karp-Lipton collapse results
Information and Computation
Oblivious symmetric alternation
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
A note on zero error algorithms having oracle access to one NP query
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
| Hi-index | 0.00 |
Via competing provers, we show that if a language A is self-reducible and has polynomial-size circuits then S2A = S2. Building on this, we strengthen the K盲mper-AFK Theorem, namely, we prove that if NP 驴 (NP 驴 coNP)/poly then the polynomial hierarchy collapses to S2NP驴coNP. We also strengthen Yap's Theorem, namely, we prove that if NP 驴 coNP/poly then the polynomial hierarchy collapses to S2NP. Under the same assumptions, the best previously known collapses were to ZPPNP and ZPPNPNP respectively ([20,6], building on [18,1,17,30]). It is known that S2 驴 ZPPNP [8]. That result and its relativized version show that our new collapses indeed improve the previously known results. Since the K盲mper-AFK Theorem and Yap's Theorem are used in the literature as bridges in a variety of results--ranging from the study of unique solutions to issues of approximation--our results implicitly strengthen all those results.