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More lCCS

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Théophile Bastian 2016-07-21 12:30:56 +01:00
parent 47f6a1880c
commit 090c60b4f1
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@ -456,31 +456,14 @@ execution, and one can synchronize processes on channels.
\begin{figure}[h]
\begin{align*}
\seman{\proc} = \seman{\chan} &\eqdef \begin{tikzpicture}[baseline]
\node (1) at (0,0.5) [draw=red,ellipse] {call};
\node (2) at (0,-0.5) [draw=green,ellipse] {done};
\draw [->] (1) -- (2);
\end{tikzpicture}
&
\seman{0} &\eqdef \begin{tikzpicture}[baseline]
\node (1) at (0,0.2) [draw=red,ellipse] {call};
\end{tikzpicture}
&
\seman{1} &\eqdef \begin{tikzpicture}[baseline]
\node (1) at (0,0.5) [draw=red,ellipse] {call};
\node (2) at (0,-0.5) [draw=green,ellipse] {done};
\draw [->] (1) -- (2);
\end{tikzpicture}
&
\end{align*}\vspace{-1.5em}\begin{align*}
\seman{P \parallel Q} &\eqdef \left(
\begin{tikzpicture}[baseline, scale=0.8]
\node (4) at (0,0.5) [draw=green,ellipse] {callP};
\node (5) at (0,-0.5) [draw=red,ellipse] {doneP};
\node (2) at (2.5,0.5) [draw=green,ellipse] {callQ};
\node (3) at (2.5,-0.5) [draw=red,ellipse] {doneQ};
\node (0) at (5,0.5) [draw=red,ellipse] {call};
\node (1) at (5,-0.5) [draw=green,ellipse] {done};
\node (4) at (0,0.65) [draw=green,ellipse] {callP};
\node (5) at (0,-0.65) [draw=red,ellipse] {doneP};
\node (2) at (2.5,0.65) [draw=green,ellipse] {callQ};
\node (3) at (2.5,-0.65) [draw=red,ellipse] {doneQ};
\node (0) at (5,0.65) [draw=red,ellipse] {call};
\node (1) at (5,-0.65) [draw=green,ellipse] {done};
\path[->]
(0) edge (1)
edge [bend right] (2)
@ -490,7 +473,56 @@ execution, and one can synchronize processes on channels.
(3) edge [bend right] (1)
(5) edge [bend right] (1);
\end{tikzpicture}
\right) \strComp \left(\seman{P} \parallel \seman{Q}\right)
\right) \strComp \left(\seman{P} \parallel \seman{Q}\right) &
\seman{\proc} = \seman{\chan} &\eqdef \begin{tikzpicture}[baseline]
\node (1) at (0,0.5) [draw=red,ellipse] {call};
\node (2) at (0,-0.5) [draw=green,ellipse] {done};
\draw [->] (1) -- (2);
\end{tikzpicture}
\\ %%%%%%%%%%%%%%%%%%%%%%%%%
\seman{P \cdot Q} &\eqdef \left(
\begin{tikzpicture}[baseline,scale=0.8]
\node (4) at (0,0.65) [draw=green,ellipse] {callP};
\node (5) at (0,-0.65) [draw=red,ellipse] {doneP};
\node (2) at (2.5,0.65) [draw=green,ellipse] {callQ};
\node (3) at (2.5,-0.65) [draw=red,ellipse] {doneQ};
\node (0) at (5,0.65) [draw=red,ellipse] {call};
\node (1) at (5,-0.65) [draw=green,ellipse] {done};
\path[->]
(0) edge (1)
edge [bend right] (4)
(2) edge (3)
(4) edge (5)
(3) edge [bend right] (1)
(5) edge (2);
\end{tikzpicture}
\right) \strComp \left(\seman{P} \parallel \seman{Q}\right) &
\seman{1} &\eqdef \begin{tikzpicture}[baseline]
\node (1) at (0,0.5) [draw=red,ellipse] {call};
\node (2) at (0,-0.5) [draw=green,ellipse] {done};
\draw [->] (1) -- (2);
\end{tikzpicture}
\\ %%%%%%%%%%%%%%%%%%%%%%%%%
\seman{(a : \chan) \cdot P} &\eqdef \left(
\begin{tikzpicture}[baseline,scale=0.8]
\node (4) at (0,0.65) [draw=green,ellipse] {callP};
\node (5) at (0,-0.65) [draw=red,ellipse] {doneP};
\node (2) at (2.5,0.65) [draw=green,ellipse] {call\_a};
\node (3) at (2.5,-0.65) [draw=red,ellipse] {done\_a};
\node (0) at (5,0.65) [draw=red,ellipse] {call};
\node (1) at (5,-0.65) [draw=green,ellipse] {done};
\path[->]
(0) edge (1)
edge [bend right] (2)
(2) edge (3)
(4) edge (5)
(3) edge (4)
(5) edge [bend right] (1);
\end{tikzpicture}
\right) \strComp \left(\seman{P} \parallel \seman{a}\right) &
\seman{0} &\eqdef \begin{tikzpicture}[baseline]
\node (1) at (0,0.2) [draw=red,ellipse] {call};
\end{tikzpicture}
\end{align*}
\caption{CCS interpretation as strategies}\label{fig:lccs:interp}
\end{figure}