\begin{tikzpicture}[font=\small,>=Latex,
 state/.style={draw,rounded corners=2pt,minimum width=2.3cm,
   minimum height=.75cm,fill=white},
 index/.style={circle,draw,minimum size=6.5mm,inner sep=1pt},
 seed/.style={index,fill=black!15}]
\node at (6.5,4.55) {(a) One propagation step, \(4\le s\le9\)};
\node[state] (known) at (1.4,3.15) {\(v_{s-3}=0\)};
\node[state] (low) at (6.5,3.15) {\(u_s=0\)};
\node[state] (high) at (11.6,3.15) {\(v_s=0\)};
\draw[->,thick] (known)--(low)
  node[midway,above=14pt] {coefficient of \(z^{a+s}\)};
\draw[->,thick] (low)--(high)
  node[midway,above=14pt] {coefficient of \(z^{L+a+s}\)};
\node at (3.95,2.48) {\(u_s+v_{s-3}=0\)};
\node at (9.05,2.48) {\(u_s+v_s=0\)};
\node at (6.5,1.55) {(b) Three chains cover all nine indices};
\foreach \first/\second/\third/\y in {1/4/7/.65,2/5/8/-.25,3/6/9/-1.15}{
  \node[seed] (first\first) at (3,\y) {\(\first\)};
  \node[index] (second\first) at (6.5,\y) {\(\second\)};
  \node[index] (third\first) at (10,\y) {\(\third\)};
  \draw[->] (first\first)--(second\first);
  \draw[->] (second\first)--(third\first);
}
\node[align=center] at (6.5,-2)
  {Index \(s\) means \(u_s=v_s=0\). Shading marks the initial zeros.};
\end{tikzpicture}