I am trying to draw a Moore machine with TikZ. This is what I have so far:
\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,positioning}
\begin{document}
\begin{tikzpicture}[>=latex',shorten >=1pt,node distance=3cm,on grid,auto]
\node[state,initial] (q0-e) {$q_0/\epsilon$};
\node[state] (q0-1) [below right=of q0-e] {$q_0'/1$};
\node[state] (q1-0) [above right=of q0-1] {$q_1/0$};
\node[state] (q2-1) [below right=of q1-0] {$q_2/1$};
\node[state,accepting] (q3-0) [below left=of q0-1] {$q_3/0$};
\node[state,accepting] (q3-1) [below right=of q0-1] {$q_3'/1$};
\path[->] (q0-e) edge node {a} (q1-0);
\path[->] (q0-e) edge node {b} (q3-0);
\path[->] (q0-1) edge node {a} (q1-0);
\path[->] (q0-1) edge [bend right] node {b} (q3-0);
\path[->] (q1-0) edge [bend left=90,looseness=2.5] node {a} (q3-1);
\path[->] (q1-0) edge node {b} (q2-1);
\path[->] (q2-1) edge node {a} (q0-1);
\path[->] (q2-1) edge node {b} (q3-1);
\path[->] (q3-0) edge node {a} (q3-1);
\path[->] (q3-0) edge [bend right] node {b} (q0-1);
\path[->] (q3-1) edge [loop below] node {a} (q3-1);
\path[->] (q3-1) edge node {b} (q0-1);
\end{tikzpicture}
\end{document}
And it produces the automaton below:

But I would like to have the edge from $q_1/0$ to $q_3'/1$ to pass "outside" the automaton, like shown by the red line of the following picture:

Can anyone show how to achieve that? Thanks.

.. controlspath operator or with for example thebend leftto path oroutandin. You already used something similar in the diagram. – Qrrbrbirlbel Dec 03 '13 at 13:27