Communications of the ACM
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Almost everywhere high nonuniform complexity
Journal of Computer and System Sciences
Cryptographic limitations on learning Boolean formulae and finite automata
Journal of the ACM (JACM)
Cryptographic lower bounds for learnability of Boolean functions on the uniform distribution
Journal of Computer and System Sciences
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
The quantitative structure of exponential time
Complexity theory retrospective II
Mathematical metaphysics of randomness
Theoretical Computer Science - Special issue Kolmogorov complexity
Complexity theoretic hardness results for query learning
Computational Complexity
A Generalization of Resource-Bounded Measure, with Application to the BPP vs. EXP Problem
SIAM Journal on Computing
Machine Learning
Machine Learning
Superpolynomial Circuits, Almost Sparse Oracles and the Exponential Hierarchy
Proceedings of the 12th Conference on Foundations of Software Technology and Theoretical Computer Science
Pseudorandom generators, measure theory, and natural proofs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Online Learning and Resource-Bounded Dimension: Winnow Yields New Lower Bounds for Hard Sets
SIAM Journal on Computing
Efficient learning algorithms yield circuit lower bounds
Journal of Computer and System Sciences
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This article extends and improves the work of Fortnow and Klivans [2009], who showed that if a circuit class C has an efficient learning algorithm in Angluin’s model of exact learning via equivalence and membership queries [Angluin 1988], then we have the lower bound EXPNP not C. We use entirely different techniques involving betting games [Buhrman et al. 2001] to remove the NP oracle and improve the lower bound to EXP not C. This shows that it is even more difficult to design a learning algorithm for C than the results of Fortnow and Klivans [2009] indicated. We also investigate the connection between betting games and natural proofs, and as a corollary the existence of strong pseudorandom generators. Our results also yield further evidence that the class of Boolean circuits has no efficient exact learning algorithm. This is because our separation is strong in that it yields a natural proof [Razborov and Rudich 1997] against the class. From this we conclude that an exact learning algorithm for Boolean circuits would imply that strong pseudorandom generators do not exist, which contradicts widely believed conjectures from cryptography. As a corollary we obtain that if strong pseudorandom generators exist, then there is no exact learning algorithm for Boolean circuits.