A deterministic finite automaton (DFA) separates two strings w and x if it accepts w and rejects x. The minimum number of states required for a DFA to separate w and x is denoted by sep(w, x). The present paper shows that the difference ∣∣sep(w, x)− sep(w, xR)∣∣ is unbounded for a binary alphabet; here w stands for the mirror image of w. This solves an open problem stated in [Demaine, Eisenstat...