"Equality" problem in distributed computation I recently started learning about distributed computation on graphs (not to be confused with parallel computation with threads).
I have seen as a side note in a few lower bound proofs, a reference that says the proof could be shorter using the &quot;linear lower bound theorem for the Equality problem&quot;, but I couldn't find the statement or proof of this theorem.
I would like to know a few things:

What exactly is this &quot;Equality&quot; problem? (how is it formulated?)
Where can I find a proof for its lower bound? (or if the proof is short enough, I would be glad if you could add it here)

Thanks!
This is probably referring to the communication complexity of the function $f(x,y) = 1$ if $x=y$ and $f(x,y) = 0$ if $x \ne y$.  See https://en.wikipedia.org/wiki/Communication_complexity#Example:_%7F'%22%60UNIQ--postMath-00000031-QINU%60%22'%7F for the formulation and a proof of the lower bound.