Alice and Bob want to know if two strings of length n are
almost equal. That is, do they differ on at most a bits?
Let 0\le a\le n-1.
We show that any deterministic protocol, as well as any
error-free quantum protocol (C^* version), for this problem
requires at least n-2 bits of communication.
We show the same bounds for the problem of determining
if two strings differ in exactly a bits.
We also prove a lower bound of n/2-1 for error-free Q^* quantum protocols.
Our results are obtained by lower-bounding the ranks of the
appropriate matrices.