 
Summary: Algebrization: A New Barrier in Complexity Theory
Scott Aaronson
MIT
aaronson@csail.mit.edu
Avi Wigderson
Institute for Advanced Study
avi@ias.edu
ABSTRACT
Any proof of P = NP will have to overcome two barriers:
relativization and natural proofs. Yet over the last decade,
we have seen circuit lower bounds (for example, that PP does
not have linearsize circuits) that overcome both barriers
simultaneously. So the question arises of whether there
is a third barrier to progress on the central questions in
complexity theory.
In this paper we present such a barrier, which we call alge
braic relativization or algebrization. The idea is that, when
we relativize some complexity class inclusion, we should give
the simulating machine access not only to an oracle A, but
also to a lowdegree extension of A over a finite field or ring.
