1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
|
% Copyright 2006 by Till Tantau
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Free Documentation License.
%
% See the file doc/generic/pgf/licenses/LICENSE for more details.
\section{Petri-Net Drawing Library}
\begin{tikzlibrary}{petri}
This packages provides shapes and styles for drawing Petri nets.
\end{tikzlibrary}
\subsection{Places}
The package defines a style for drawing places of Petri nets.
\begin{stylekey}{/tikz/place}
This style indicates that a node is a place of a Petri net. Usually,
the text of the node should be empty since places do not contain any
text. You should use the |label| option to add text outside the node
like its name or its capacity. You should use the |tokens| options,
explained in Section~\ref{section-tokens}, to add tokens inside the
place.
\begin{codeexample}[]
\begin{tikzpicture}
\node[place,label=above:$p_1$,tokens=2] (p1) {};
\node[place,label=below:$p_2\ge1$,right=of p1] (p2) {};
\end{tikzpicture}
\end{codeexample}
\begin{stylekey}{/tikz/every place}
This style is evoked by the style |place|. To change the
appearance of places, you can change this style.
\begin{codeexample}[]
\begin{tikzpicture}
[every place/.style={draw=blue,fill=blue!20,thick,minimum size=9mm}]
\node[place,tokens=7,label=above:$p_1$] (p1) {};
\node[place,structured tokens={3,2,9},
label=below:$p_2\ge1$,right=of p1] (p2) {};
\end{tikzpicture}
\end{codeexample}
\end{stylekey}
\end{stylekey}
\subsection{Transitions}
Transitions are also nodes. They should be drawn using the following
style:
\begin{stylekey}{/tikz/transition}
This style indicates that a node is a transition. As for places, the
text of a transition should be empty and the |label| option should
be used for adding labels.
To connect a transition to places, you can use the |edge| command as
in the following example:
\begin{codeexample}[]
\begin{tikzpicture}
\node[place,tokens=2,label=above:$p_1$] (p1) {};
\node[place,label=above:$p_2\ge1$,right=of p1] (p2) {};
\node[transition,below right=of p1,label=below:$t_1$] {}
edge[pre] (p1)
edge[post] node[auto] {2} (p2);
\end{tikzpicture}
\end{codeexample}
\begin{stylekey}{/tikz/every transition}
This style is evoked by the style |transition|.
\end{stylekey}
\begin{stylekey}{/tikz/pre}
This style can be used with paths leading \emph{from} a transition
\emph{to} a place to indicate that the place is in the pre-set of
the transition. By default, this style is |<-,shorten <=1pt|, but
feel free to redefine it.
\end{stylekey}
\begin{stylekey}{/tikz/post}
This style is also used with paths leading \emph{from} a transition
\emph{to} a place, but this time the place is in the post-set of
the transition. Again, feel free to redefine it.
\end{stylekey}
\begin{stylekey}{/tikz/pre and post}
This style is to be used to indicate that a place is both in the
pre- and post-set of a transition.
\end{stylekey}
\end{stylekey}
\subsection{Tokens}
\label{section-tokens}
Interestingly, the most complicated aspect of drawing Petri nets in
\tikzname\ turns out to be the placement of tokens.
Let us start with a single token. They are also nodes and there is a
simple style for typesetting them.
\begin{stylekey}{/tikz/token}
This style indicates that a node is a token. By default, this causes
the node to be a small black circle. Unlike places and transitions,
it \emph{does} make sense to provide text for the token node. Such
text will be typeset in a tiny font and in white on black
(naturally, you can easily change this by setting the style
|every token|).
\begin{codeexample}[]
\begin{tikzpicture}
\node[place,label=above:$p_1$] (p1) {};
\node[token] at (p1) {};
\node[place,label=above:$p_2$,right=of p1] (p2) {};
\node[token] at (p2) {$y$};
\end{tikzpicture}
\end{codeexample}
\begin{stylekey}{/tikz/every token}
Change this style to change the appearance of tokens.
\end{stylekey}
\end{stylekey}
In the above example, it is bothersome that we need an extra command
for the token node. Worse, when we have \emph{two} tokens on a node,
it is difficult to place both nodes inside the node without overlap.
The Petri net library offers a solution to this problem: The
|children are tokens| style.
\begin{stylekey}{/tikz/children are tokens}
The idea behind this style is to use trees mechanism for placing
tokens. Every token lying on a place is treated as a child of the
node. Normally this would have the effect that the tokens are placed
below the place and they would be connected to the place by an
edge. The |children are tokens| style, however, redefines the growth
function of trees such that it places the children next to each
other inside (or, rather, on top) of the place node. Additionally,
the edge from the parent node is not drawn.
\begin{codeexample}[]
\begin{tikzpicture}
\node[place,label=above:$p_1$] {}
[children are tokens]
child {node [token] {1}}
child {node [token] {2}}
child {node [token] {3}};
\end{tikzpicture}
\end{codeexample}
In detail, what happens is the following: Tree growth functions tell
\tikzname\ where it should place the children of nodes. These
functions get passed the number of children that a node has an the
number of the child that should be placed. The special tree growth
function for tokens has a special mapping for each possible number
of children up to nine children. This mapping decides for each child
where it should be placed on top of the place. For example, a single
child is placed directly on top of the place. Two children are
placed next to each other, separated by the |token distance|. Three
children are placed in a triangle whose side lengths are
|token distance|; and so on up to nine tokens. If you wish to place
more than nice tokens on a place, you will have to write your own
placement code.
\begin{codeexample}[]
\begin{tikzpicture}
\node[place,label=above:$p_2$] {}
[children are tokens]
child {node [token] {1}}
child {node [token,fill=red] {2}}
child {node [token,fill=red] {2}}
child {node [token] {1}};
\end{tikzpicture}
\end{codeexample}
\begin{key}{/tikz/token distance=\meta{distance}}
This specifies the distance between the centers of the tokens in the
arrangements of the option |children are tokens|.
\begin{codeexample}[]
\begin{tikzpicture}
\node[place,label=above:$p_3$] {}
[children are tokens,token distance=1.1ex]
child {node [token] {}}
child {node [token,red] {}}
child {node [token,blue] {}}
child {node [token] {}};
\end{tikzpicture}
\end{codeexample}
\end{key}
\end{stylekey}
The |children are tokens| option gives you a lot of flexibility, but
it is a bit cumbersome to use. For this reason there are some options
that help in standard situations. They all use |children are tokens|
internally, so any change to, say, the |every token| style will
affect how these options depict tokens.
\begin{key}{/tikz/tokens=\meta{number}}
This option is given to a |place| node, not to a |token| node. The
effect of this option is to add \meta{number} many child nodes to
the place, each having the style |token|. Thus, the following two
pieces of codes have the same effect:
\begin{codeexample}[]
\tikz
\node[place] {}
[children are tokens]
child {node [token] {}}
child {node [token] {}}
child {node [token] {}};
\tikz
\node[place,tokens=3] {};
\end{codeexample}
It is legal to say |tokens=0|, no tokens are drawn in this
case. This option does not handle ten or more tokens correctly. If
you need this many tokens, you will have to program your own code.
\begin{codeexample}[]
\begin{tikzpicture}[every place/.style={minimum size=9mm}]
\foreach \x/\y/\tokennumber in {0/2/1,1/2/2,2/2/3,
0/1/4,1/1/5,2/1/6,
0/0/7,1/0/8,2/0/9}
\node [place,tokens=\tokennumber] at (\x,\y) {};
\end{tikzpicture}
\end{codeexample}
\end{key}
\begin{key}{/tikz/colored tokens=\meta{color list}}
This option, which must also be given when a place node is being
created, gets a list of colors as parameter. It will then add as
many tokens to the place as there are colors in this list, each filled correspondingly.
\begin{codeexample}[]
\tikz \node[place,colored tokens={black,black,red,blue}] {};
\end{codeexample}
\end{key}
\begin{key}{/tikz/structured tokens=\meta{token texts}}
This option, which must again be passed to a place, gets a list of
texts for tokens. For each text, a new token will be added to the place.
\begin{codeexample}[]
\tikz \node[place,structured tokens={$x$,$y$,$z$}] {};
\end{codeexample}
\begin{codeexample}[]
\begin{tikzpicture}[every place/.style={minimum size=9mm}]
\foreach \x/\y/\tokennumber in {0/2/1,1/2/2,2/2/3,
0/1/4,1/1/5,2/1/6,
0/0/7,1/0/8,2/0/9}
\node [place,structured tokens={1,...,\tokennumber}] at (\x,\y) {};
\end{tikzpicture}
\end{codeexample}
If you use lots of structured tokens, consider redefining the
|every token| style so that the tokens are larger.
\end{key}
\subsection{Examples}
\begin{codeexample}[]
\begin{tikzpicture}[yscale=-1.6,xscale=1.5,thick,
every transition/.style={draw=red,fill=red!20,minimum size=3mm},
every place/.style={draw=blue,fill=blue!20,minimum size=6mm}]
\foreach \i in {1,...,6} {
\node[place,label=left:$p_\i$] (p\i) at (0,\i) {};
\node[place,label=right:$q_\i$] (q\i) at (8,\i) {};
}
\foreach \name/\var/\vala/\valb/\height/\x in
{m1/m_1/f/t/2.25/3,m2/m_2/f/t/2.25/5,h/\mathit{hold}/1/2/4.5/4} {
\node[place,label=above:{$\var = \vala$}] (\name\vala) at (\x,\height) {};
\node[place,yshift=-8mm,label=below:{$\var = \valb$}] (\name\valb) at (\x,\height) {};
}
\node[token] at (p1) {}; \node[token] at (q1) {};
\node[token] at (m1f) {}; \node[token] at (m2f) {};
\node[token] at (h1) {};
\node[transition] at (1.5,1.5) {} edge [pre] (p1) edge [post] (p2);
\node[transition] at (1.5,2.5) {} edge [pre] (p2) edge[pre] (m1f)
edge [post](p3) edge[post] (m1t);
\node[transition] at (1.5,3.3) {} edge [pre] (p3) edge [post] (p4)
edge [pre and post] (h1);
\node[transition] at (1.5,3.7) {} edge [pre] (p3) edge [pre] (h2)
edge [post] (p4) edge [post] (h1.west);
\node[transition] at (1.5,4.3) {} edge [pre] (p4) edge [post] (p5)
edge [pre and post] (m2f);
\node[transition] at (1.5,4.7) {} edge [pre] (p4) edge [post] (p5)
edge [pre and post] (h2);
\node[transition] at (1.5,5.5) {} edge [pre] (p5) edge [pre] (m1t)
edge [post] (p6) edge [post] (m1f);
\node[transition] at (1.5,6.5) {} edge [pre] (p6) edge [post] (p1.south east);
\node[transition] at (6.5,1.5) {} edge [pre] (q1) edge [post] (q2);
\node[transition] at (6.5,2.5) {} edge [pre] (q2) edge [pre] (m2f)
edge [post] (q3) edge [post] (m2t);
\node[transition] at (6.5,3.3) {} edge [pre] (q3) edge [post] (q4)
edge [pre and post] (h2);
\node[transition] at (6.5,3.7) {} edge [pre] (q3) edge [pre] (h1)
edge [post] (q4) edge [post] (h2.east);
\node[transition] at (6.5,4.3) {} edge [pre] (q4) edge [post] (q5)
edge [pre and post] (m1f);
\node[transition] at (6.5,4.7) {} edge [pre] (q4) edge [post] (q5)
edge [pre and post] (h1);
\node[transition] at (6.5,5.5) {} edge [pre] (q5) edge [pre] (m2t)
edge [post] (q6) edge [post] (m2f);
\node[transition] at (6.5,6.5) {} edge [pre] (q6) edge [post] (q1.south west);
\end{tikzpicture}
\end{codeexample}
Here is the same net once more, but with these styles changes:
\begin{codeexample}[code only]
\begin{tikzpicture}[yscale=-1.1,thin,>=stealth,
every transition/.style={fill,minimum width=1mm,minimum height=3.5mm},
every place/.style={draw,thick,minimum size=6mm}]
\end{codeexample}
\begin{tikzpicture}[yscale=-1.1,thin,>=stealth,
every transition/.style={fill,minimum width=1mm,minimum height=3.5mm},
every place/.style={draw,thick,minimum size=6mm}]
\foreach \i in {1,...,6} {
\node[place,label=left:$p_\i$] (p\i) at (0,\i) {};
\node[place,label=right:$q_\i$] (q\i) at (8,\i) {};
}
\foreach \name/\var/\vala/\valb/\height/\x in
{m1/m_1/f/t/2.25/3,m2/m_2/f/t/2.25/5,h/\mathit{hold}/1/2/4.5/4} {
\node[place,label=above:{$\var = \vala$}] (\name\vala) at (\x,\height) {};
\node[place,yshift=-8mm,label=below:{$\var = \valb$}] (\name\valb) at (\x,\height) {};
}
\node[token] at (p1) {}; \node[token] at (q1) {};
\node[token] at (m1f) {}; \node[token] at (m2f) {};
\node[token] at (h1) {};
\node[transition] at (1.5,1.5) {} edge [pre] (p1) edge [post] (p2);
\node[transition] at (1.5,2.5) {} edge[pre] (p2) edge[pre] (m1f)
edge[post] (p3) edge[post] (m1t);
\node[transition] at (1.5,3.3) {} edge [pre] (p3) edge [post] (p4)
edge [pre and post] (h1);
\node[transition] at (1.5,3.7) {} edge [pre] (p3) edge [pre] (h2)
edge [post] (p4) edge [post] (h1.west);
\node[transition] at (1.5,4.3) {} edge [pre] (p4) edge [post] (p5)
edge [pre and post] (m2f);
\node[transition] at (1.5,4.7) {} edge [pre] (p4) edge [post] (p5)
edge [pre and post] (h2);
\node[transition] at (1.5,5.5) {} edge [pre] (p5) edge [pre] (m1t)
edge [post] (p6) edge [post] (m1f);
\node[transition] at (1.5,6.5) {} edge [pre] (p6) edge [post] (p1.south east);
\node[transition] at (6.5,1.5) {} edge [pre] (q1) edge [post] (q2);
\node[transition] at (6.5,2.5) {} edge [pre] (q2) edge [pre] (m2f)
edge [post] (q3) edge [post] (m2t);
\node[transition] at (6.5,3.3) {} edge [pre] (q3) edge [post] (q4)
edge [pre and post] (h2);
\node[transition] at (6.5,3.7) {} edge [pre] (q3) edge [pre] (h1)
edge [post] (q4) edge [post] (h2.east);
\node[transition] at (6.5,4.3) {} edge [pre] (q4) edge [post] (q5)
edge [pre and post] (m1f);
\node[transition] at (6.5,4.7) {} edge [pre] (q4) edge [post] (q5)
edge [pre and post] (h1);
\node[transition] at (6.5,5.5) {} edge [pre] (q5) edge [pre] (m2t)
edge [post] (q6) edge [post] (m2f);
\node[transition] at (6.5,6.5) {} edge [pre] (q6) edge [post] (q1.south west);
\end{tikzpicture}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "pgfmanual-pdftex-version"
%%% End:
|
