Automate fini déterministe en TikZ — états, transitions, état acceptant

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{automata, positioning, arrows.meta}

\begin{document}
\begin{tikzpicture}[
  shorten >=1pt, node distance=2.6cm, on grid, auto, font=\sffamily,
  every state/.style={
    fill=blue!10, draw=blue!60!black, thick, minimum size=12mm
  },
  initial/.style={initial text=, initial by arrow},
  accepting/.style={fill=green!15, draw=green!50!black,
                    double, double distance=2pt}
]
  \node[state, initial]            (q0)                     {$q_0$};
  \node[state]                     (q1) [right=of q0]       {$q_1$};
  \node[state]                     (q2) [right=of q1]       {$q_2$};
  \node[state, accepting]          (q3) [right=of q2]       {$q_3$};

  \path[->, thick]
    (q0) edge              node {a} (q1)
    (q1) edge              node {b} (q2)
    (q2) edge              node {a} (q3)
    (q1) edge [bend left, blue!70!black]  node[above] {a} (q3)
    (q3) edge [loop above, red!70!black]  node {b} ()
    (q0) edge [loop above]                node {b} ()
    (q2) edge [bend right, below]         node {b} (q0);

  \node[above=4mm of q1.north, font=\footnotesize\itshape, anchor=south] {Automate fini déterministe sur $\{a, b\}$};

\end{tikzpicture}
\end{document}