Quelle drawing.xml Sprache: XML

<?xml version="1.0" encoding="UTF-8"?>
 <Appendix>
 <Heading>
 Drawing automata
 </Heading>
 The drawing of graphs described here uses
 <C>graphviz</C> <Cite Key="KoutsofiosNorth:2002"/>, a software for drawing graphs developed at AT
 <Alt Only="LaTeX">
 \&
 </Alt>
 <Alt Not="LaTeX">
 <Alt Only="HTML">
 &
 </Alt>
 <Alt Not="HTML">
 &
 </Alt>
 </Alt>
 T Labs, that can be obtained at
 <URL>https://www.graphviz.org/</URL>.


 <Section>
 <Heading>
 Installing some external programs
 </Heading>
 In order to create the drawings you should have <URL Text="graphviz">https://www.graphviz.org/</URL>
 installed and to view them you should have installed some <C>pdf</C> viewer.
 </Section>

 <Section>
 <Heading>
 Functions to draw automata
 </Heading>

 <ManSection>
 <Func Arg="A [state_names, L]" Name="DrawAutomaton" />
 <Description>
 This function draws automaton
 <A>A</A>.
 The arguments <A>state_names</A>, <A>L</A> and <A>file</A> are optional.

 
 An automaton with <C>n</C> states will be drawn with numbers <C>1</C> to <C>n</C>
 written inside the corresponding graph node.
 The argument <A>state_names</A> is a list of <C>n</C> strings which will be the new text
 written inside the corresponding graph node.

 
 The argument <A>L</A> is a list of lists of integers, each of which specifies a set
 of states to be drawn in a different color.

</Description>
 </ManSection>
<Example><![CDATA[
gap> x:=Automaton("det",3,2,[ [ 2, 3, 0 ], [ 0, 1, 2 ] ],[ 1 ],[ 1, 2, 3 ]);;
gap> DrawAutomaton(x);

gap> DrawAutomaton(x,["st 1", "2", "C"]);

gap> DrawAutomaton(x,["st 1", "2", "C"],[[2],[1,3]]);
]]></Example>
The output of the three previous <C>DrawAutomaton</C> commands would be the following diagrams,
respectively.

 <Alt Only="LaTeX">
 \begin{figure}[htbp] \begin{center} \leavevmode \includegraphics[bb=0 0 74 250]{aut2.jpg} \end{center} \label{fig:aut2} \end{figure}
 </Alt>
 <Alt Only="HTML">
 <center><img src="aut2.jpg"></center> 
 </Alt>
 
 <Alt Only="LaTeX">
 \begin{figure}[htbp] \begin{center} \leavevmode \includegraphics[bb=0 0 100 250]{aut2_1.jpg} \end{center} \label{fig:aut2_1} \end{figure}
 </Alt>
 <Alt Only="HTML">
 <center><img src="aut2_1.jpg"></center> 
 </Alt>
 
 <Alt Only="LaTeX">
 \begin{figure}[htbp] \begin{center} \leavevmode \includegraphics[bb=0 0 100 250]{aut2_2.jpg} \end{center} \label{fig:aut2_2} \end{figure}
 </Alt>
 <Alt Only="HTML">
 <center><img src="aut2_2.jpg"></center> 
 </Alt>

 <ManSection>
 <Func Arg="arg" Name="DotForDrawingAutomaton" />
 <Description>
 This function computes the dot code that can be used to display an automaton. This can be done by using the function <Ref Func="DrawAutomaton" /> (if the system is properly configured) or by the user in some independent way. The arguments and options are the same than those of <Ref Func="DrawAutomaton" />.
 </Description>
 </ManSection>
 <Example><![CDATA[
gap> DotStringForDrawingAutomaton(x);
"digraph Automaton{\n\"1\" -> \"2\" [label=\"a\",color=red];\n\"2\" -> \"3\" \
[label=\"a\",color=red];\n\"2\" -> \"1\" [label=\"b\",color=blue];\n\"3\" -> \
\"2\" [label=\"b\",color=blue];\n\"1\" [shape=triangle,peripheries=2, style=fi\
lled, fillcolor=white];\n\"2\" [shape=doublecircle, style=filled, fillcolor=wh\
ite];\n\"3\" [shape=doublecircle, style=filled, fillcolor=white];\n}\n"
 ]]></Example>
 By using Print (or PrinTo, if one wants to print to a file) the string is displayed as follows:
 <Example><![CDATA[
gap> Print(last);
digraph Automaton{
"1" -> "2" [label="a",color=red];
"2" -> "3" [label="a",color=red];
"2" -> "1" [label="b",color=blue];
"3" -> "2" [label="b",color=blue];
"1" [shape=triangle,peripheries=2, style=filled, fillcolor=white];
"2" [shape=doublecircle, style=filled, fillcolor=white];
"3" [shape=doublecircle, style=filled, fillcolor=white];
}
]]></Example>
 The dot code produced for the remaining pictures:
 <Example><![CDATA[
gap> Print(DotStringForDrawingAutomaton(x,["st 1", "2", "C"]));
digraph Automaton{
"st 1" -> "2" [label="a",color=red];
"2" -> "C" [label="a",color=red];
"2" -> "st 1" [label="b",color=blue];
"C" -> "2" [label="b",color=blue];
"st 1" [shape=triangle,peripheries=2, style=filled, fillcolor=white];
"2" [shape=doublecircle, style=filled, fillcolor=white];
"C" [shape=doublecircle, style=filled, fillcolor=white];
}
gap> Print(DotStringForDrawingAutomaton(x,["st 1", "2", "C"],[[2],[1,3]]));
digraph Automaton{
"st 1" -> "2" [label="a",color=red];
"2" -> "C" [label="a",color=red];
"2" -> "st 1" [label="b",color=blue];
"C" -> "2" [label="b",color=blue];
"st 1" [shape=triangle,peripheries=2, style=filled, fillcolor=burlywood];
"2" [shape=doublecircle, style=filled, fillcolor=brown];
"C" [shape=doublecircle, style=filled, fillcolor=burlywood];
}
]]></Example>
 <ManSection>
 <Func Arg="A, B" Name="DrawSubAutomaton" />
 <Description>
 This function tests if automaton
 <C>
 A
 </C>
 is a subautomaton of
 <C>
 B
 </C>
 in which case draws
 <C>
 B
 </C>
 highlighting the edges not in
 <C>
 A
 </C>
 by drawing them in a dotted style, while the others are drawn in a plain style.
 </Description>
 </ManSection>
<Example><![CDATA[
gap> A := Automaton("nondet",5,"abc",[ [ [ 2, 3 ], [ 5 ], [ 1, 4, 5 ], [ 1, 5 ],
[ 3, 4 ] ], [ [ 1, 4, 5 ], [ ], [ 1 ], [ 1, 3, 5 ], [ 1, 2, 5 ] ], [ [ ],
[ 2, 4, 5 ], [ 1, 3, 5 ], [ ], [ 2, 3, 4 ] ] ],[ ],[ 2, 3, 4 ]);;
gap> B := Automaton("nondet",5,"abc",[ [ [ 2, 3 ], [ 5 ], [ 1, 4, 5 ], [ 1, 5 ],
[ 3, 4 ] ], [ [ 1, 4, 5 ], [ ], [ 1 ], [ 1, 3, 5 ], [ 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 ]);;
gap> DrawSubAutomaton(A,B);
]]></Example>
The output is as follows, in case the configuration of your computer permits. Otherwise, you may be interested in the dot code, as pshown below.

<Alt Only="LaTeX">
 \begin{center}
 \includegraphics[width=0.5\textwidth]{subaut.jpg}
 \end{center}
 </Alt>
 <Alt Only="HTML">
 <center><img src="subaut.jpg"></center> 
 </Alt>
 
 <ManSection>
 <Func Arg="A, B" Name="DotStringForDrawingSubAutomaton" />
 <Description>
 This function computes the dot code that can be used to draw automata A, with the subsutomaton B emphasized. It is silently used by the function <Ref Func="DrawSubAutomaton" /> (if the system is properly configured) or can be used by the user in some independent way.
 </Description>
 </ManSection>
 <Example><![CDATA[
gap> DotStringForDrawingSubAutomaton(A,B);
"digraph Automaton {\n1 -> 2 [label=\"a\",color=red];\n1 -> 3 [label=\"a\",co\
lor=red];\n1 -> 1 [label=\"b\",color=blue];\n1 -> 4 [label=\"b\",color=blue];\
\n1 -> 5 [label=\"b\",color=blue];\n1 -> 1 [label=\"c\",color=green,style = do\
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=\
\"c\",color=green];\n2 -> 4 [label=\"c\",color=green];\n2 -> 5 [label=\"c\",co\
lor=green];\n3 -> 1 [label=\"a\",color=red];\n3 -> 4 [label=\"a\",color=red];\
\n3 -> 5 [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 -> 1 [label=\"b\",color=blue];\n4 -> 3 [label=\"b\",color=blue];\n4 ->\
5 [label=\"b\",color=blue];\n4 -> 2 [label=\"c\",color=green,style = dotted];\
\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 [label=\"a\",color=red];\n5 -> 4 [label=\"a\",color=red];\n5 -> 1 [label=\"\
b\",color=blue];\n5 -> 2 [label=\"b\",color=blue];\n5 -> 5 [label=\"b\",color=\
blue];\n5 -> 2 [label=\"c\",color=green];\n5 -> 3 [label=\"c\",color=green];\n\
5 -> 4 [label=\"c\",color=green];\n3 [shape=triangle,color=gray];\n4 [shape=tr\
iangle,color=gray];\n5 [shape=triangle,color=gray];\n2 [shape=doublecircle];\n\
3 [shape=doublecircle];\n4 [shape=doublecircle];\n1 [shape=circle];\n}\n"
 ]]></Example>
 By using Print (or PrinTo, if one wants to print to a file) the string is displayed as follows:
 <Example><![CDATA[
gap> Print(last);
digraph Automaton {
1 -> 2 [label="a",color=red];
1 -> 3 [label="a",color=red];
1 -> 1 [label="b",color=blue];
1 -> 4 [label="b",color=blue];
1 -> 5 [label="b",color=blue];
1 -> 1 [label="c",color=green,style = dotted];
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 -> 1 [label="b",color=blue];
3 -> 1 [label="c",color=green];
3 -> 3 [label="c",color=green];
3 -> 5 [label="c",color=green];
4 -> 1 [label="a",color=red];
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 -> 2 [label="c",color=green,style = dotted];
4 -> 3 [label="c",color=green,style = dotted];
4 -> 4 [label="c",color=green,style = dotted];
4 -> 5 [label="c",color=green,style = dotted];
5 -> 3 [label="a",color=red];
5 -> 4 [label="a",color=red];
5 -> 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 [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];
}
]]></Example>
 <ManSection>
 <Func Arg="G" Name="DotStringForDrawingGraph" />
 <Func Arg="G" Name="DrawGraph" />
 <Description>
 Draws a graph specified as an adjacency list
 <C>G</C>.
 </Description>
 </ManSection>
 <Example><![CDATA[
gap> G := [[1,2,3],[5],[3,4],[1],[2,5]];
[ [ 1, 2, 3 ], [ 5 ], [ 3, 4 ], [ 1 ], [ 2, 5 ] ]
gap> Print(DotStringForDrawingGraph(G));
digraph Graph__{
1 -> 1 [style=bold, color=black];
1 -> 2 [style=bold, color=black];
1 -> 3 [style=bold, color=black];
2 -> 5 [style=bold, color=black];
3 -> 3 [style=bold, color=black];
3 -> 4 [style=bold, color=black];
4 -> 1 [style=bold, color=black];
5 -> 2 [style=bold, color=black];
5 -> 5 [style=bold, color=black];
1 [shape=circle];
2 [shape=circle];
3 [shape=circle];
4 [shape=circle];
5 [shape=circle];
}
]]></Example>
 The dot code can be used to produce the following picture (which may also be produced by typing <Code>DrawGraph(G);</Code>
 <Alt Only="LaTeX">
 \begin{center}
 \includegraphics[width=0.45\textwidth]{graph2.pdf}
 \end{center}
 </Alt>

 <Alt Only="HTML">
 <center><img src="graph2.jpg"></center> 
 </Alt>
<ManSection>
 <Func Arg="A [state_names, L]" Name="DrawSCCAutomaton" />
 <Description>
 Draws automaton
 <C>
 A
 </C>
 and highlights it's strongly connected components by drawing the other edges in a dotted style.
 
 The optional arguments <A>state_names</A> and <A>L</A> are as described in
 <Ref Func="DrawAutomaton" />.
 </Description>
</ManSection>
 <Example><![CDATA[
gap> rcg := Automaton("det",6,"ab",[ [ 3, 3, 6, 5, 6, 6 ], [ 4, 6, 2, 6, 4, 6 ] ],
[ ],[ ]);;
gap> Print(DotStringForDrawingSCCAutomaton(rcg));
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];
}
]]></Example>
 The dot code can be used to produce the following picture (which may also be produced by typing <Code>DrawGraph(G);</Code>
 <Alt Only="LaTeX">
 \begin{center}
 \includegraphics[width=0.45\textwidth]{sccpoi2.pdf}
 \end{center}
 </Alt>

 <Alt Only="HTML">
 <center><img src="sccpoi2.jpg"></center> 
 </Alt>

 </Section>

 </Appendix>

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