New Lower Bounds against Homogeneous Non-Commutative Circuits

01/04/2023

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by   Prerona Chatterjee, et al.

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We give several new lower bounds on size of homogeneous non-commutative circuits. We present an explicit homogeneous bivariate polynomial of degree d which requires homogeneous non-commutative circuit of size Ω(d/log d). For an n-variate polynomial with n>1, the result can be improved to Ω(nd), if d≤ n, or Ω(nd log n/log d), if d≥ n. Under the same assumptions, we also give a quadratic lower bound for the ordered version of the central symmetric polynomial.