no code implementations • 3 Dec 2020 • Srinivasan Arunachalam, Alex B. Grilo, Tom Gur, Igor C. Oliveira, Aarthi Sundaram
This result is optimal in both $\gamma$ and $T$, since it is not hard to learn any class $\mathfrak{C}$ of functions in (classical) time $T = 2^n$ (with no error), or in quantum time $T = \mathsf{poly}(n)$ with error at most $1/2 - \Omega(2^{-n/2})$ via Fourier sampling.
no code implementations • 3 Nov 2016 • Igor C. Oliveira, Rahul Santhanam
We prove several results giving new and stronger connections between learning, circuit lower bounds and pseudorandomness.
no code implementations • 30 Oct 2014 • Eric Blais, Clément L. Canonne, Igor C. Oliveira, Rocco A. Servedio, Li-Yang Tan
In this paper we study the structure of Boolean functions in terms of the minimum number of negations in any circuit computing them, a complexity measure that interpolates between monotone functions and the class of all functions.