TR23-001 Authors: Prerona Chatterjee, Pavel Hrubes

Publication: 5th January 2023 14:43

Downloads: 112

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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 $\Omega(d/\log d)$. For an $n$-variate polynomial with $n>1$, the result can be improved to $\Omega(nd)$, if $d\leq n$, or $\Omega(nd \frac{\log n}{\log d})$, if $d\geq n$.

Under the same assumptions, we also give a quadratic lower bound for the ordered version of the central symmetric polynomial.