Communications of the ACM
Finite monoids and the fine structure of NC1
Journal of the ACM (JACM)
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
SIAM Journal on Computing
On learning ring-sum-expansions
SIAM Journal on Computing
On learning embedded symmetric concepts
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Depth reduction for circuits of unbounded fan-in
Information and Computation
The power of the middle bit of a #P function
Journal of Computer and System Sciences
Computational Complexity - Special issue on circuit complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Concrete Mathematics: A Foundation for Computer Science
Concrete Mathematics: A Foundation for Computer Science
Automata Theory Meets Circuit Complexity
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Separating the polynomial-time hierarchy by oracles
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
| Hi-index | 0.00 |
A midbit function on l binary inputs x1, ..., xl outputs the middle bit in the binary representation of x1 + ... + xl. We consider the problem of PAC learning embedded midbit functions, where the set S 驴 {x1, ..., xn} of relevant variables on which the midbit depends is unknown to the learner.To motivate this problem, we first show that a polynomial time learning algorithm for the class of embedded midbit functions would immediately yield a fairly efficient (quasipolynomial time) PAC learning algorithm for the entire complexity class ACC. We then give two different subexponential learning algorithms, each of which learns embedded midbit functions under any probability distribution in 2驴n log n time. Finally, we give a polynomial time algorithm for learning embedded midbit functions under the uniform distribution.