On ε-biased generators in NC⁰

A pseudorandom generator is an efficient deterministic procedure that maps a shorter random input into a longer output that is indistinguishable from the uniform distribution by resource-bounded observers. Cryan and Miltersen recently considered the question of whether there can be a pseudorandom generator in NC⁰, that is, a pseudorandom generator that maps n bits strings to m bits strings and such that every bit of the output depends on a constant number k of bits of the seed. It is shown that for k = 3, if m ≥ 4n + 1, it is possible to break the generator with a linear test.