In my class a student asked whether all finite automata could be drawn without crossing edges (it seems all my examples did). Of course the answer is negative, the obvious automaton for the language $\{\; x\in\{a,b\}^* \mid \#_a(x)+2\#_b(x) \equiv 0 \mod 5 \;\}$ has the structure of $K_5$, the co...