On the gap between separating words and separating their reversals

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(wR,xR)| is unbounded for a binary alphabet; here wR stands for the mirror image of w. This solves an open problem stated in Demaine et al. (2011) [2].