# Randomized Identity testing for circuits

$$(1)$$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 $$(2)$$