Lower bounds for non-commutative skew circuits

@article{Limaye2015LowerBF,
  title={Lower bounds for non-commutative skew circuits},
  author={Nutan Limaye and Guillaume Malod and Srikanth Srinivasan},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2015},
  volume={22},
  pages={22}
}
Nisan (STOC 1991) exhibited a polynomial which is computable by linear sized noncommutative circuits but requires exponential sized non-commutative algebraic branching programs. Nisan’s hard polynomial is in fact computable by linear sized skew circuits (skew circuits are circuits where every multiplication gate has the property that all but one of its children is an input variable or a scalar). We prove that any non-commutative skew circuit which computes the square of the polynomial defined… CONTINUE READING
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