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      Drawing automata
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<"ChapSects"<href".html#> span =>
      Drawing automata
    </span></a>
<div class="java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 6
          programs
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</div>
<div class="ContSect"><span class="tocline"><span classjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
        Functionsjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
      </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><      <
< "< /<class="> n;/< java.lang.StringIndexOutOfBoundsException: Range [74, 73) out of bounds for length 147
<span class="ContSS"><br /><span class="nocss">  </span><a href="chapB_mj.html#X84DF99868747DD69">B.2-3 DrawSubAutomaton</a></span>
<span class=
pidXjava.lang.StringIndexOutOfBoundsException: Range [29, 27) out of bounds for length 62
span"java.lang.StringIndexOutOfBoundsException: Range [21, 19) out of bounds for length 141
</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

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

<h4>B.1 <p java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 183
        Installing programs
      </span></h4>

<p>In order to create the drawings you should have <span class="URL"><a href="https://www.graphviz.org/">graphviz</a></span> installed and to view them you should have java.lang.StringIndexOutOfBoundsException: Index 170 out of bounds for length 0

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

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

<p><a id="X7BC2FDA77FD0237B" name="X7BC2FDA77FD0237B"></a></p>

<h5>B.2-1 DrawAutomaton</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; DrawAutomaton</code>( <var class="Arg">A</var>[, <var class="Arg">state_names</var>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
Arg"><var>and <ar class=Arg"="DrawAutomatonx;/span>

<p>An automaton with

<p>The argument <var class="Arg">L</var> is a list of lists of integers, <


<div class="example"><pre>
<span class="GAPprompt">gap>pre>/>
< =GAPprompt>apgt<span span ="DrawAutomaton)</spanjava.lang.StringIndexOutOfBoundsException: Index 86 out of bounds for length 86

<span class="GAPprompt">gap></span> <span class="GAPinput">DrawAutomaton(x,["st 1", "2", "C"]);</span

<span class=<>>imgsrc"j"</<br</>
</pre></div>

<>output   previous <code class=c><code>commands bethe  diagrams .</

<p><br><center><img java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 0

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

<p><br><center><img src="aut2_2.jpg"></center><br></p>

<>< =X7896CAD4832C7748"=X7896CAD4832C7748"<a>p

<h5>B.2-2 span =GAPprompt>&;/> < classjava.lang.StringIndexOutOfBoundsException: Range [62, 60) out of bounds for length 101

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"[label\"\colorred]\\2"-\1\[=
<p>This function"2"[=\"b"c=]\\1"[triangle,peripheries2 fi\


<div class="example"><pre>
<pan class=GAPprompt>ap&;</span>< =GAPinput>(x;</pan>
"digraph  Automaton{\n\</></>
[label=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
\2\ [abel"\"color=lue;n"1[=triangle,=2,style=fi\
lled, fillcolor=white];\n\"2\" [shape=doublecircle, style=filled, fillcolor=wh\
ite];\n\"3\" [shape=doublecircle, style=filled, fillcolor=java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 0
       </re<divjava.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18

<p>By using Print (or PrinTo, if one wants to print to a file) the2"-;""[abel=a"colorred];


<class=">pre>
<span class="GAPprompt">gap1"shape=,peripheries2 =filled,fillcolorwhite];
digraphAutomaton
"1" -> "2" [label=" shape= = fillcolor=white]
"" -gt;""[abel"",olorred;
"2" -> "1" [label="b",color=blue];
""-g " label=b,color=];
"1" [java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 0
"2" [shape=span class="GAPprompt&t;/>spanclass=GAPinput>PrintD(x,[st1,"" C]);<>
"3" [shape=doublecircle, style=filled, fillcolor=white];
}
</pre></div>

<pThe  codeproduced forthe remaining pictures:/>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">Print(DotStringForDrawingAutomaton(x,["st 1", "2", "C"]));</span>
digraph  Automaton{
"st 1" -> "2" [label="a",color=red];
2" >" [abel"",olor=]java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
"" -;"t1"[=,=]
"C" -> "2" [label="b",color"t "[triangle=,stylefilled white;
"st 1" [shape="2" [shape=doublecirclstyle=illed fillcolor;
"=filled,fillcolor=hite]java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
"" [hapedoublecircle =illed,fillcolorwhite;
}
<span class="GAPprompt">gap></span> <span class="GAPinput">Print" 1 -gt;""[=a,color=ed;
digraph  Automaton{
""2"-;" 1"[=b,color=blue]
"" -gt;" l=""=]java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
"2 gt;"t1 label=b,=]
"C" -> "2" [label="b",color=blue];
" 1 shape=,=2sjava.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for length 73
" shape=,style=,fillcolor=]java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
"C"[hape java.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds for length 60
}
pre>/ivjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12

<p><a id="X84DF99868747DD69" name="X84DF99868747DD69"></a></p>

<h5>B.2-3 DrawSubAutomaton</h5>

<div class=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<p>This function tests if automaton <code class=GAPinput": ""5,,   ,3 ,[5 , , ,5] [ ,5],</span>


<div class="example"><pre>
<span class="GAPprompt"><span class="GAPprompt">gap  ][[1 ,5] [ ]  1][ 1 ,5 ], [1 ,  ,  ,
[ 3, 4 ] ], [ [,4, 5 ,[1, 3,5 ]   ,3, 4 ]]][] 2,3  );
[ 2,4  ,[1,3 5] ,  2,3,  ]], , 2,3,4];java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
<span class="GAPprompt">gap></span> <span class="GAPinput">B := Automaton("nondet",5,"abc",[ [ [ 2, 3 ], [ 5 ], [ 1, 4, 5 ], [ 1, 5 ],<[3,  ]],[1, ,5] []1, ,,5]  1,2 5 ],[ , ,5 ]
[ 3, 4 ]span"GAPprompt"gap&;/>< class"APinput"DrawSubAutomaton,)<span>
[ 2, 4, 5 ], [ 1, java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
< class=GAPprompt"gap&;</><span class="APinput>DrawSubAutomatonA);/>
</pre></div>

<p>The output is as follows, in java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 0

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

<p><a id="X7BB5015378320678" name

<h5>B.2-4 DotStringForDrawingSubAutomaton</h5>

<div class="func"><<iv class="unc"<table=func 100%"><>td =tdleft">code class=func"&8227DotStringForDrawingSubAutomaton<code>(var class=Arg"A/>,<varclass
<p>This function computes the dot code that can be used to It is silently  function < =f"DrawSubAutomaton</ode>(a href"hapB_mj.html#84DF99868747DD69>spanclass="">B.23<span</>  the  is properly configured)orcan be used by the user in some independent way.</p>


<div span classGAPprompt>&t</pan>span ="APinput"DotStringForDrawingSubAutomatonB;/java.lang.StringIndexOutOfBoundsException: Index 106 out of bounds for length 106
<span class="GAPprompt">gap></span> <span lor=red]\-g;1=b"color=]\n1 >  label=\b\,color=;java.lang.StringIndexOutOfBoundsException: Index 84 out of bounds for length 84
"digraph  Automaton {\n1 -> 2 [label=\"a\",color=red];\n1 -> 3 [label=\"a\",co\
lorred]\1->  [abel="b\"color=blue];\n1 -> 4 [label=\"b\",color=blue];\
\n1 -> 5 [label=\"b\",color=blue];color=green,style = dotted];\n2 -> 5 [label=\"a\",color=red];\n2 -> 2 [label=\
tted];\n1 -> 4 [label=\"c\",color=green,style = dotted];\n1 -> 5 [label=\"c\",\
color=green,style = dotted];\n2 -> 5 [label=\"a\",color=red];\n2 -> 2 [label=\
\"\n3-&t;5[label=\"a\",color=red];\n3 -> 1 [label=\"b\",color=blue];\n3 -> 1 [l\
lor=green];n3-&t  [abel\"\",olor=red];\n3 -> 4 [label=\"a\",color=red];\
\ [label=\"a\",color=red];\n3 -> 1 [label=\"b\",color=blue];\n3 -> 1 [l\
abel\c\"color=green];\n3 -> 3 [label=\"c\",color=green];\n3 -> 5 [label=\"c\
\",color=green];\n4 -> 1 [label=\"a\",color=red];\n4 -> 5 [label=\"a\",color=r\
ed]\n4 -gt 1[label=\"b\",color=blue];\n4 -> 3 [label=\"b\",color=blue];\n4 ->\
 5 [label=\"b\",color=blue];\n4 -> 2 [label=n &t;3[label=\c\"=reen,style = dotted];\n4 -> 4 [label=\"c\",color=\
\n4 -> 3 [label=\"c\",color=green,style = dotted];\n4 -> 4 [label=\"c\",color=\
green,style = dotted];\n4 -> 5 [label=\"c\",color=green,style = dotted];\n5 ->\
 3 [\blue\ -;2 [label"\,color=blue];\n5 -> 5[label=\"b\",color=\
b"color=blue];n5 -gt; 2[label=\b\,color=blue]\n5 -&t; 5 [abel==\b\,color=\
blue];\n5 -> 2 [label=\"c\",color=green];\n5 -> 3 [label=\"c\",color=green];\n\
5-gt;4[label="\",olorgreen]\3[=riangle,color=ray]n [hapetrjava.lang.StringIndexOutOfBoundsException: Index 82 out of bounds for length 82
iangle shape=doublecircle];\n4 [shape=doublecircle];\n1 [shape=circle];\n}\"
3 [shape=doublecircle];\n4 [shape=doublecircle];\n1 [shape=circle];\n}\n"
      </pre></div>

<>By Print(rPrinTo,ifonewants toprint to a file)thestring is displayed as follows:</p>


<div class="example">
<span="GAPprompt">gap></span> <span class="GAPinput">Print(last);</span>
igraph  Automaton {
1 -> 2 [label="a",color=red];
1 -> 3 [label="a",colordigraph  Automaton {
1 -> 1 [label="b",color=blue];
1 -&t 4 [label="",olorblue];
1 -> 5 [label="b",color=blue];
1 -> 1 [label="c",1 -> 3 [label="a",color&t 3[label="",color=red]
1 -> 4 [label="c",color=green,style = dotted];
1 -> 5 [label="c",color=green,style = dotted];
2 -> 5 [label="a",color=red];
2 -> 2 [label="c",color=green];
2 -> 4 [label="c",color=green];
2 > 5 [label="c",color=green];
3 -> 1 [label="a",color=red];
3 > 4 [label="a",color=red];
3 -> 5 [label="a",color=red];
3 -gt;1[=b,olor=]java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
3 -> 1 [label="c",color=green];
3 -> 3 [label="c",color=green];
3 -> 5 [label="c",color=green];
 & 1 [abel="",olor=ed;
4 -> 5 [label="a",color=red];
4 -> 1 [label="b",color=blue];
4 -> 3 [label="b",color=blue];
4 -> 5 [label="b",color=blue];
4 -gt2 [=c,color=green,style = dotted];
4 -> 3 [label="c",color=green,style = dotted];
 -gt 4 [label="c",color=green,style = dotted];
4 -> 5 [label="c",color=green3 -gt; 5  [label="c",color=green];
5];
5 -> 4 [label="a",color=red];
5 -gt; 1 [label="b",color=blue];
5 -> 2 [label="b",color=blue];
5 -> 5 [label="b",color=blue];
5 > 2 [label="c",color=green];
5 -> 3 [label="c",color=green];
5 -> 4 [label="c",color=green];
3 [,color=ray]java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
4 [shape=triangle,color=gray];
5 [shape=triangle,color=gray];
2 [shape=doublecircle];
3 [shape=doublecircle];
4pe=oublecircle];
1 [shape=circle];
}
</re></div>

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

<B2- DotStringForDrawingGraph

<lass=func"<tableclass="func" width="100%"><tr><td class="tdleft"><code class="func">‣ DotStringForDrawingGraph</code>( <var class="Arg">G</var> )</td><td class="tdright">( function )5-&t; 5[abel=b,color=blue]java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
<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>
<>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 := [[1,2,3],[5],[3,4],[1],[2,5]];</span>
[ [ 1, 2, 3 ], [ 5 ], [ 3, 4 ], [ 1digraph Graph__{
<span class="GAPprompt">gap></span> <span class="GAPinput">Print(DotStringForDrawingGraph> 2 style=old color=lack]java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
digraph Graph__{
1 -> 1 [style=bold, color=black];
1 -> 2 [style=bold, color=black];
1 -=bold, color=black]java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
2 > 5 [tyle=,color=black];
3 -> 3 [style=bold, color=black];
3 -> 4 [style=bold, color=black5 gt;5 [tyle=, color=black];
4 -> 1 [style=bold, color=black];
5  -&t 2 [style=bold, color=black];
5 -> 5 [style=bold, color=black];
1 [shape=circle];
2 [shape=circle];
3 [hapecircle];
4 [shape=circle];
5 [shape=circle];

</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="graph2.jpg"></center><br></p>

<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="<p>he 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="graph2.jpg"></center><br></p>

<hr />
<p class="java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 0
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