In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 − c lower bound ...
We describe a new approach for understanding the difficulty of designing efficient learning algorithms. We prove that the existence of an efficient learning algorithm for a circui...
—In 1982, Kannan showed that ΣP 2 does not have nk -sized circuits for any k. Do smaller classes also admit such circuit lower bounds? Despite several improvements of Kannan’s...
Boolean functions on the space Fm 2 are not only important in the theory of error-correcting codes, but also in cryptography. In these two cases, the nonlinearity of these functio...
—A space bounded Stack Machine is a regular Turing Machine with a read-only input tape, several space bounded read-write work tapes, and an unbounded stack. Stack Machines with a...