Algebrization: A New Barrier in Complexity Theory

@article{Aaronson2009AlgebrizationAN,
  title={Algebrization: A New Barrier in Complexity Theory},
  author={Scott Aaronson and Avi Wigderson},
  journal={ACM Trans. Comput. Theory},
  year={2009},
  volume={1},
  pages={2:1-2:54}
}
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 (e.g., that PP does not have linear-size 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 article, we present such a barrier, which we call algebraic relativization or algebrization. The idea is that, when we… 
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