The random oracle hypothesis is false
Journal of Computer and System Sciences
An Exact Characterization of Symmetric Functions in qAC0[2]
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
On Learning Embedded Midbit Functions
ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
Circuit Bottom Fan-in and Computational Power
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
A Lower Bound For Perceptrons And An Oracle Separation Of The PP/sup PH/ Hierarchy
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Upper and Lower Bounds for Some Depth-3 Circuit Classes
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Hardness amplification proofs require majority
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On the constant-depth complexity of k-clique
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Learning Deep Architectures for AI
Foundations and Trends® in Machine Learning
On the Power of Small-Depth Computation
Foundations and Trends® in Theoretical Computer Science
Amplifying lower bounds by means of self-reducibility
Journal of the ACM (JACM)
Conformant plans and beyond: Principles and complexity
Artificial Intelligence
Why Does Unsupervised Pre-training Help Deep Learning?
The Journal of Machine Learning Research
Distributionally-hard languages
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
BQP and the polynomial hierarchy
Proceedings of the forty-second ACM symposium on Theory of computing
Cracks in the defenses: scouting out approaches on circuit lower bounds
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Higher complexity search problems for bounded arithmetic and a formalized no-gap theorem
Archive for Mathematical Logic
On the expressive power of deep architectures
ALT'11 Proceedings of the 22nd international conference on Algorithmic learning theory
Lower bounds for circuits with few modular and symmetric gates
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the correlation between parity and modular polynomials
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Extractors and Lower Bounds for Locally Samplable Sources
ACM Transactions on Computation Theory (TOCT)
Random access to advice strings and collapsing results
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
On the power of unambiguity in alternating machines
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Determinism versus nondeterminism with arithmetic tests and computation: extended abstract
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Computing symmetric boolean functions by circuits with few exact threshold gates
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
"Resistant" polynomials and stronger lower bounds for depth-three arithmetical formulas
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Graph Isomorphism is Not AC0-Reducible to Group Isomorphism
ACM Transactions on Computation Theory (TOCT)
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We present exponential lower bounds on the size of depth-k Boolean circuits for computing certain functions. These results imply that there exists an oracle set A such that, relative to A, all the levels in the polynomial-time hierarchy are distinct, i.e., ΣkP,A is properly contained in Σk+1P,A for all k.