Tighter Connections between Derandomization and Circuit Lower Bounds

We tighten the connections between circuit lower bounds and derandomization for each of the following three types of derandomization: general derandomization of promise-BPP (connected to Boolean circuits), derandomization of Polynomial Identity Testing (PIT) over fixed finite fields (connected to arithmetic circuit lower bounds over the same field), and derandomization of PIT over the integers (connected to arithmetic circuit lower bounds over the integers). We show how to make these connections uniform equivalences, although at the expense of using somewhat less common versions of complexity classes and for a less studied notion of inclusion. Our main results are as follows:

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Marco Carmosino, Russell Impagliazzo, Valentine Kabanets, Antonina Kolokolova
• Keywords: Algorithms, APPROX 2015