We initiate the study of the space complexity of property testing. We focus on five properties of Boolean functions that have been intensively studied in the property testing literature: monotonicity, symmetry, linearity, being a junta, and being a linear threshold function.

On the upper bounds side, we show --- ... more >>>

Feedforward neural networks with sigmoid activations are of fundamental importance in neural computation. However, our understanding of the circuit complexity of such networks for implementing Boolean functions remains limited. The analog output of the sigmoid, along with its transcendental nature, leads to unique mathematical challenges for proving lower bounds.

... more >>>

We show that over the field of rational numbers, there is a deterministic algorithm for factorization of constant depth circuits that makes calls to a (whitebox or blackbox) PIT algorithm for such circuits. The time complexity of the algorithm (and hence the number of calls to the PIT oracle) is ... more >>>