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$(1)$If a Arithmetic circuit $C$ has a size $x$, the degree $f_C$ should be $ \leq 2^{x-1} $? Is this bound sharp? why?

$(2)$By fingerprinted polynomial Evaluation how to determine the degree of two circuits $f_C$ and $f_{C'}$ are identical.

N.B.: Please add some references. I'm trying to find an randomized algorithm for $(2)$

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