Non-commutative circuits and the sum-of-squares problem

  title={Non-commutative circuits and the sum-of-squares problem},
  author={Pavel Hrubes and Avi Wigderson and Amir Yehudayoff},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
We initiate a direction for proving lower bounds on the size of non-commutative arithmetic circuits. This direction is based on a connection between lower bounds on the size of <i>non-commutative</i> arithmetic circuits and a problem about <i>commutative</i> degree four polynomials, the classical sum-of-squares problem: find the smallest n such that there exists an identity (x<sub>1</sub><sup>2</sup>+x<sub>2</sub><sup>2</sup>+•• + x<sub>k</sub><sup>2</sup>)• (y<sub>1</sub>^2+y<sub>2</sub><sup>2… CONTINUE READING
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