1 research outputs found
Derandomizing Polynomial Identity over Finite Fields Implies Super-Polynomial Circuit Lower Bounds for NEXP
We show that derandomizing polynomial identity testing over an arbitrary
finite field implies that NEXP does not have polynomial size boolean circuits.
In other words, for any finite field F(q) of size q, , where is the polynomial
identity testing problem over F(q), and NSUBEXP is the nondeterministic
subexpoential time class of languages. Our result is in contract to Kabanets
and Impagliazzo's existing theorem that derandomizing the polynomial identity
testing in the integer ring Z implies that NEXP does have polynomial size
boolean circuits or permanent over Z does not have polynomial size arithmetic
circuits