"Equality" problem in distributed computation
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.