fig-three-cases.tex

\documentclass[tikz,border=7pt]{standalone}
\usepackage[T1]{fontenc}
\usepackage{lmodern,amsmath,amssymb}
\hyphenpenalty=10000
\exhyphenpenalty=10000
\usetikzlibrary{arrows.meta,positioning,calc,fit,backgrounds}
\definecolor{ink}{HTML}{243B4A}
\definecolor{pale}{HTML}{EFF5F7}
\definecolor{warm}{HTML}{FAF5E8}
\tikzset{every node/.style={font=\sffamily\small,text=ink},
 box/.style={draw=ink!65,rounded corners=2pt,fill=pale,align=center,inner sep=7pt},
 warmbox/.style={box,fill=warm},
 arr/.style={-{Latex[length=2mm]},draw=ink!80,line width=.65pt},
 lab/.style={font=\sffamily\footnotesize,fill=white,inner sep=2pt},
 dot/.style={circle,draw=ink!75,fill=white,minimum size=8mm,inner sep=1pt},
 title/.style={font=\sffamily\bfseries\small,align=center}}
\begin{document}\begin{tikzpicture}

\node[box,text width=5cm] (test) at (6,6.5) {Does $\ell$ begin with the arriving letter $a$?};
\node[warmbox,text width=4.4cm] (ext) at (1.6,4.2) {\textbf{External}\\$\ell=a\ell_0$\\$P'=aPa,\quad\ell'=\ell_0$};
\node[box,text width=5cm] (inner) at (9,4.2) {Does $D_a(P)$ exist?};
\node[warmbox,text width=4.4cm] (dir) at (6.3,1.5) {\textbf{Internal}\\$P'=aD_a(P)a$\\$\ell'=\omega_a(P)\ell$};
\node[warmbox,text width=3.8cm] (reset) at (11.4,1.5) {\textbf{Reset}\\$P'=\epsilon$\\$\ell'=aP\ell$};
\draw[arr] (test.south west)--node[lab,above left]{yes}(ext.north);
\draw[arr] (test.south east)--node[lab,above right]{no}(inner.north);
\draw[arr] (inner.south west)--node[lab,above left]{yes}(dir.north);
\draw[arr] (inner.south east)--node[lab,above right]{no}(reset.north);

\end{tikzpicture}\end{document}