The complexity of optimization problems
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
The Boolean hierarchy I: structural properties
SIAM Journal on Computing
The polynomial time hierarchy collapses if the Boolean hierarchy collapses
SIAM Journal on Computing
The Boolean hierarchy II: applications
SIAM Journal on Computing
SIAM Journal on Computing
Bounded queries to SAT and the Boolean hierarchy
Theoretical Computer Science
On the structure of bounded queries to arbitrary NP sets
SIAM Journal on Computing
On Bounded Queries and Approximation
SIAM Journal on Computing
A Downward Collapse within the Polynomial Hierarchy
SIAM Journal on Computing
Journal of Computer and System Sciences
Bounded queries, approximations, and the Boolean hierarchy
Information and Computation
The Boolean Hierarchy and the Polynomial Hierarchy: A Closer Connection
SIAM Journal on Computing
Counting, Selecting, adn Sorting by Query-Bounded Machines
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
FCT '85 Fundamentals of Computation Theory
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A Tight Karp-Lipton Collapse Result in Bounded Arithmetic
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Nondeterministic Instance Complexity and Proof Systems with Advice
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
A tight Karp-Lipton collapse result in bounded arithmetic
ACM Transactions on Computational Logic (TOCL)
Proof systems that take advice
Information and Computation
| Hi-index | 0.00 |
The results in this paper show that coNP is contained in NP with 1 bit of advice (denoted NP/1) if and only if the Polynomial Hierarchy (PH) collapses to DP, the second level of the Boolean Hierarchy (BH). Previous work showed that BH 驴 DP 驴 coNP 驴 NP/poly. The stronger assumption that PH 驴 DP in the new result allows the length of the advice function to be reduced to a single bit and also makes the converse true. The one-bit case can be generalized to any constant k: PH 驴 BH2k 驴 coNP 驴 NP/k where BH2k denotes the 2k-th level of BH and NP/k denotes the class NP with k-bit advice functions.