<?xml version="1.0" encoding="UTF-8"?>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
         "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<script type="text/javascript"
  src="https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<title>GAP (Automata) - Appendix B: 
      Drawing automata
    </title>
<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
<meta name="generator" content="GAPDoc2HTML" />
<link rel="stylesheet" type="text/css" href="manual.css" />
<script src="manual.js" type="text/javascript"></script>
<script type="text/javascript">overwriteStyle();</script>
</head>
<body class="chapB"  onload="jscontent()">


<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chap5_mj.html">5</a>  <a href="chap6_mj.html">6</a>  <a href="chapA_mj.html">A</a>  <a href="chapB_mj.html">B</a>  <a href="chapC_mj.html">C</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

<div=mjs"type=text"</scriptjava.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56

<p id="mathjaxlink" class="pcenter"><a href="chapB.html">[MathJax off]</a></p>
<p><a id="X82D249F0793E6561" name="X82D249F0793E6561"></a></p>
<div class="ChapSects"><a href="chapB_mj.html#X82D249F0793E6561">B <span class="Heading">
      Drawing automata
    </span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapB_mj.html#X7988DBAB78EA0C06">B.1 <span class="Heading">
        Installing some external programs
      </span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapB_mj.html#X84C97CA079719B11">B.2 <span class="Heading">
        Functions to draw automata
      </span></a>
</span>
<java.lang.StringIndexOutOfBoundsException: Range [0, 4) out of bounds for length 0

<span class="ContSS"><br /><span class="nocss">  </span><a href="chapB_mj.html#X7896CAD4832C7748">B.2-2 DotForDrawingAutomaton</a></span>
<pan java.lang.StringIndexOutOfBoundsException: Range [20, 19) out of bounds for length 141
<span ">B.2-4 DotStringForDrawingSubAutomaton/><span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapB_mj.html#X7870774E83892026">B.2-5 DotStringForDrawingGraph</a></span>
<span div class=ChapSects>a href="hapB_mjX82D249F0793E6561"B<span class"Heading"
</div></div>
</div>

<h3>B <span class="Heading">
      Drawing automata
    </span></h3>

<p>The drawing of graphs described here uses <code class="code">graphviz</code> <a hrefInstallingsomeexternal programs

<p><a id="X7988DBAB78EA0C06" name="X7988DBAB78EA0C06"></a></p>

<h4>B.1 <span class="Heading">
        Installing java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 7
      </span><h4>

<p>In order spanclass="ContSS"br/span "nocss"&bsp<span>ahref="chapB_mj.html#X7896CAD4832C7748">B.2-2 DotForDrawingAutomaton</a></span>

<p><a id="X84C97CA079719B11" name="X84C97CA079719B11"></a></p>

<h4>B.2 <span class="Heading">
        Functions to draw automata
      </span></h4>

<p><a ="7BC2FDA77FD0237B" name="X7BC2FDA77FD0237B"></a></p>

<h5>B. class="ContSS"><br /><span class="nocss">  </span><a href="chapB_mj.html#X7E478FDD807853CA">B.2-6 java.lang.StringIndexOutOfBoundsException: Index 119 out of bounds for length 12

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227
<p>Thisfunction draws automaton <var class="Arg">A</var>. The arguments <var class="Arg">state_names</var>, <var class="Arg">L<Installing someexternal 

<p>An automaton with <code class="code">n</code> states will be drawn with numbers <code class="code">1</code> to <code class="code">n</code> written inside the corresponding graph node. The argument <var class="Arg">state_names</var> is a list of <code class="code">n</code> strings which will be the new text written inside the corresponding graph node.</p>

<p>The argument <var class="Arg">L</var> is a list of lists of integers, each of which specifies a set of states to be drawn in a different color.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">x:=Automaton("det",3,2,[ [ 2, 3, 0 ], [ 0, 1, 2 ] ],[ 1 ],[Arg"L/ <ar ">file<</var> are optional.</p>
<span class="GAPprompt">gap></span> <span class=GAPinput"()</span>

<java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0

<span class="GAPprompt">gap></span> <span class="GAPinput">DrawAutomaton(x,["st 
</</iv>

<p>The outputspanclass=">&;/span>< class=GAPinput>(x;>

<p><br><center><img src="aut2.jpg"></center><br></p>

<p><br><center><img src="aut2_1.jpg"></center><br></p>

<p>br>center>img =aut2_2.pg></center>>p>

<p><a id=<The output ofthethreepreviousclass"ode"DrawAutomaton<  would   following,respectively/>

<h5>B.2-2 DotForDrawingAutomaton</h5>

<java.lang.StringIndexOutOfBoundsException: Range [0, 4) out of bounds for length 0
<p>This function computes the dot code that can be used to display an java.lang.StringIndexOutOfBoundsException: Index 73 out of bounds for length 0


<divp>aid=X7896CAD4832C7748"name=X7896CAD4832C7748>/>/>
<class"APprompt"gap&t<span> span class="GAPinput">DotStringForDrawingAutomaton(x);</span>
"digraph  Automaton{\java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
[=\"",=;n"2\ -gt; "1\ [abel\"b\",color=blue];\n\"3\" -> \
\2\ label\,olorblue]n"\ shape=triangle,=2,style=\
lled, fillcolor=whitejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
ite];\n\< class"">&t>spanclass""DotStringForDrawingAutomaton)</pan
      prediv

<p>By using Print (or PrinTo, if one wants to print to a \2\ [=\b"=lue]\n\1\" [hape,eripheries,stylejava.lang.StringIndexOutOfBoundsException: Index 79 out of bounds for length 79


<div class="example"><pre>
<     </>/>
digraph  Automaton{
"1" -> "2" [java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 0
"2"-gt; 3" l=a"=];
"2" -> "1" [label="b",color=blue];
<iv ="xample">pre
""[triangle=,style,=];
"2" [shape=doublecircle, style=filled  {
""[hapedoublecircle,stylefilled,fillcolorwhite;
}
</2-gt 3 l=ac=]java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36

<p>The " &t;""[""colorblue;


<div class="example"><pre>
<">gapgt;span>< ="Print(otStringForDrawingAutomaton," 1" ", "");<spanjava.lang.StringIndexOutOfBoundsException: Index 127 out of bounds for length 127
digraph  Automaton>dot   the</>
"java.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 0
"2" -> "C" [label="a",  java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
"2" -> "st 1" [label="b",color=blue]"-gt; ""l=acred;
"C" ->2 -gt s 1" label=b"colorblue;
"1 shape=,peripheries2 =filled, fillcolor=]java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
"e, style=, fillcolor=white];
"C" [shape=doublecircle, 2" [shape=doublecircle, style =;
}
<spanCs=,style=illed =]
digraph  java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1
st1"- "" label="",color=]
"2" -> "C" [label="a",color=red];
" > "st1" [abel=b",]
""" & C"[abel=""color=red;
"st 1" [shape=triangle,peripheries=2, style=filled2"-&;s 1"[abel=b"color==lue]
"2" [shape=doublecirclest"[=riangle,peripheries2, tyle=filled, fillcolor=burlywood];
"C" ""[doublecircle filled brown;
}
</pre></div"shape=doublecircle,style=filled, fillcolor=burlywood];

<</>/iv>

<h5>B.2-3 DrawSubAutomaton</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft
<p>This function tests if automaton <code class=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0


<div class="example"><pre>
ass=GAPinput"A =Automaton("ondet"5,abc"[[[2,3 ]  5] [1 4 5 ] [ 1  java.lang.StringIndexOutOfBoundsException: Index 144 out of bounds for length 144
[ 3, 4] ]   1,4  ]  ][1 ]  ,3 5 ] ] [, 2 5]] [[]
[2 4, 5] [  , [ ],[2 ,4   , ][2 ,4 ];
<span class="GAPprompt">gap></span> <span class="GAPinput">B := Automaton("nondet",5,2 ,5]  1,3, ,[ ], [2,3 4] ][][2 3  ]);
[, 4]],   1,4  ][] [ 1 ] [1,3  ][1,2,5  ]  [1 4 5 ]
[ 2, 4, 5 ], [ 1, 3, 5 ], [ 2, 3, 4, 5 ], [ 2, 3, 4 ] ] ],[ 3, 4, 5 ],[ 2, 3, 4 ]);;
< class=GAPprompt>&t<span spanclass=G>(AB;/>
</pre></div>

<p>The output is as follows, in case the configuration of your computer permits. Otherwise, you may be interested in span =>gt<span> class""(,B;span

<p><br><center><img src="subaut.jpg"></center><br></p>

<p><a id="X7BB5015378320678" name="X7BB5015378320678

<h5>B.2-4 java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 0

<iv=""table class="width="tr<class""> class=>#; /(<var""A</ar, class="Arg">B</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>This function computes the dot code that can be used to draw automata A, with the subsutomaton B emphasized. It  used by thefunction codeclass"unc"DrawSubAutomaton/ode (=cX84"> ="efLink.-3/>/> (ifsystemis properlyconfigured)or java.lang.StringIndexOutOfBoundsException: Range [320, 319) out of bounds for length 368


<div class="example"><pre>
<=""gapg;/pan><class=">(A,)<span>
"digraph  Automaton {\n1 -> 2 [label=\"a\",color=red];\n1 -> 3 [label=\"a\",co\
]n1 &t  [label=="\"blue;-gt 4[\\"blue]\
\n1 -> 5 [label=\"b\",color=blue];\n1 -> 1 [label=\"c\",color=green,style = do\
tted];\n1 -> 4 [label=\"c\=]n & [="java.lang.StringIndexOutOfBoundsException: Range [40, 39) out of bounds for length 84
java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 84
\"c\",color=green];\n2 -> 4 [label=\"c\",color=green];\n2 -> 5 [label=\"c\",co\
lor=green];\n3 -> 1 [label=\"a\",color=red];\n3 -> 4 [java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 84
\g; java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 88
abel=\"c\",color=green];\n3 ->\ &;1[=a,java.lang.StringIndexOutOfBoundsException: Range [46, 45) out of bounds for length 84
\",color=n3 -> 5java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 88
ed];\n4 -> 1 [label=\"b\",color=blue];\n4 -> 3 [="\,java.lang.StringIndexOutOfBoundsException: Range [25, 22) out of bounds for length 85
 5 [label=\"b\",color=blue];\n4 -> 2 [label=\"c\",;n4-; java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 88
\4-g  \,color=java.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds for length 85
green,style = dotted];\n4 -> 5 [label=\"c\",color=green,style = dotted];\n5 ->\
 3 [label=\"a\",color=red];\n5 -> 4 [label=\"a\",java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bounds for length 85
b",color=];\5-gt;2 =\b";& java.lang.StringIndexOutOfBoundsException: Range [72, 71) out of bounds for length 85
blue];\n5 -> 2 [label=\"\";5-  \";-g; l=""java.lang.StringIndexOutOfBoundsException: Range [84, 83) out of bounds for length 85
5 -> 4 [label=\"c\",color=green];\n3 [shape=triangle,color=gray];5 &;  =c"c=;n shape=,=ray]\4[=\
iangle,color=gray];\n5 [shape=triangle,color=gray];\n2 [shape=doublecircle];\n\
3[n\java.lang.StringIndexOutOfBoundsException: Index 73 out of bounds for length 73
      </pre></div>

<p>By <> using ( ,   a  java.lang.StringIndexOutOfBoundsException: Range [74, 73) out of bounds for length 102


<div  classjava.lang.StringIndexOutOfBoundsException: Range [24, 22) out of bounds for length 81
<span class="GAPprompt" java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
java.lang.StringIndexOutOfBoundsException: Range [20, 18) out of bounds for length 20
1 -> 2 [label=1&; bc=java.lang.StringIndexOutOfBoundsException: Range [32, 31) out of bounds for length 33
1 -&; a,;
1 -> 1 [label="b",color=blue];
1 -> 4 [label="b",color=blue];
1 -> 5 [label="b",color=blue];
1 -> 1 [2 -> 2 [label  =java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 34
1 -> 4 [label=-java.lang.StringIndexOutOfBoundsException: Range [7, 6) out of bounds for length 34
1 -> 5 [label="c",color-  java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 32
2 ->3&t  label""cblue;
2 -> 2 [label="c",color=green];
2 -> 4 [label="c",color=green];
2 -> 5 [label="c",color=green];
3 -> 1 [label="a",color=-gt;1 [=",olor=]
3 -> 4 [label="a",color=red];
3 -> 5 [label="a",color=red];
3 -> 1 [label="b",color=blue];
3 -> 1 [label="c4&;  label""java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 49
3 -&-;4[java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 49
3-;5[colorjava.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 34
4 -> 1 [label="a",color=5 -> 3 [label="a",color=red
4 -> ;1 java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 33
4 -> 1 [label="b",color=blue];
4 ->-java.lang.StringIndexOutOfBoundsException: Range [7, 6) out of bounds for length 34
4 -> 5 [label="b",color=blue];
4 -> 2 [[shape=triangle=;
4 -> 3 [label="c",color=green,style = dotted];
4 -> 4 ]
4 -&4 [sha=java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 23
5/>/java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
5 -> 4 [label="a",color=red];
5 -> 1 [label="bh5>.25</h5>
5 -&<div c=> java.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for length 231
 &; l=";
5 -> 2 [label="c",color=green];
5 -> 3 [label="c",color=green];
5 -> 4 [label="c",color=green];
3 [shape=triangle,color=gray];
4 [shape=triangle,color=gray];
5 [shape=triangle,color=gray];
2 [shape=doublecircle];
3 [shape=doublecircle];
4 [shape=doublecircle];
1 [shape=circle];
}
</pre></div>

<p><a id="X7870774E83892026" name="X7870774E83892026"></a></p>

<h5>B.2-5 DotStringForDrawingGraph</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; DotStringForDrawingGraph</code>( <var class="Arg">G</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; DrawGraph</code>( <var class="Arg">G</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Draws a graph specified as an adjacency list <code class="code">G</code>.</p>


<div class="example"><pre> 
<span class="GAPprompt">gap></span> <span class="GAPinput">G pa java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 80
[ [ 1, 2, 3 ], [ 5 ], [ 3, java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 104
<span class="GAPprompt">gap></span> <span class="GAPinput">Print(DotStringForDrawingGraph(G));</span>
java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
1 -> 1 [style=bold, color=black];
1 -&  =,=;
1 -> 3 [style=bold, color=black];
2 -> 5 [style=bold, color=black];
3 -> 3 [style=bold, 
3 -> 4 [style=bold, color=black];
4 -> 1 [> 3 [style ;
5 -> 2    sbold blackjava.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
 &;5[bold java.lang.StringIndexOutOfBoundsException: Range [36, 34) out of bounds for length 36
1 [shape=circle];
2 5&; java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 36
3 [shape=circle];
4 [shape=circle];
5 [shape=circle3s=java.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for length 17
}
</pre></div>

>java.lang.StringIndexOutOfBoundsException: Range [19, 15) out of bounds for length 190

<p><a id="X7E478FDD807853CA" name="X7E478FDD807853CA"></a></p>

<h5>B.2-6 DrawSCCAutomaton</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; DrawSCCAutomaton</code>( <var class="Arg">A</var>[, <var class="Arg">state_names</var>, <var class="Arg">L</var>] )</td><td class="tdright">( function )</td></tr></table></div>
<p>Draws automaton <code class="code"> A </code> and highlights it's strongly connected components by drawing the other edges in a dotted style.</p>

<p>The optional arguments <var class="Arg">state_names</var> and <var class="Arg">L</var> are as described in <code class="func">DrawAutomaton</code> (<a href="chapB_mj.html#X7BC2FDA77FD0237B"><span class="RefLink">B.2-1</span></a>).</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">rcg := Automaton("det",6,"ab",[ [ 3, 3, 6, 5, 6, 6 ], [ 4, 6, 2, 6, 4, 6 ] ],</span>
[ ],[ ]);;
<span class="GAPprompt">gap></span> <span class="GAPinput">Print(DotStringForDrawingSCCAutomaton(rcg));</span>
digraph  Automaton{
"1" -> "3" [label="a",color=red,style = dotted];
"2" -> "3" [label="a",color=red];
"3" -> "6" [label="a",color=red,style = dotted];
"4" -> "5" [label="a",color=red];
"5" -> "6" [label="a",color=red,style = dotted];
"6" -> "6" [label="a",color=red,style = dotted];
"1" -> "4" [label="b",color=blue,style = dotted];
"2" -> "6" [label="b",color=blue,style = dotted];
"3" -> "2" [label="b",color=blue];
"4" -> "6" [label="b",color=blue,style = dotted];
"5" -> "4" [label="b",color=blue];
"6" -> "6" [label="b",color=blue,style = dotted];
"1" [shape=circle, style=filled, fillcolor=white];
"2" [shape=circle, style=filled, fillcolor=white];
"3" [shape=circle, style=filled, fillcolor=white];
"4" [shape=circle, style=filled, fillcolor=white];
"5" [shape=circle, style=filled, fillcolor=white];
"6" [shape=circle, style=filled, fillcolor=white];
}
</pre></div>

<p>The dot code can be used to produce the following picture (which may also be produced by typing <code class="code">DrawGraph(G);</code> <br><center><img src="sccpoi2.jpg"></center><br></p>


<div class="chlinkprevnextbot"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chapA_mj.html">[Previous Chapter]</a>    <a href="chapC_mj.html">[Next Chapter]</a>   </div>


<div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chap5_mj.html">5</a>  <a href="chap6_mj.html">6</a>  <a href="chapA_mj.html">A</a>  <a href="chapB_mj.html">B</a>  <a href="chapC_mj.html">C</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

<hr />
<p class="foot">generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>
</body>
</html>