GAP (Automata) - Appendix B: Drawing automata

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B Drawing automata
B.1 Installing some external programs
B.2 Functions to draw automata
B.2-1 DrawAutomaton
B.2-2 DotForDrawingAutomaton
B.2-3 DrawSubAutomaton
B.2-4 DotStringForDrawingSubAutomaton
B.2-5 DotStringForDrawingGraph
B.2-6 DrawSCCAutomaton

### B Drawing automata

The drawing of graphs described here uses `graphviz` [DEG+02], a software for drawing graphs developed at AT & T Labs, that can be obtained at https://www.graphviz.org/.

#### B.1 Installing some external programs

In order to create the drawings you should have graphviz installed and to view them you should have installed some `pdf` viewer.

#### B.2 Functions to draw automata

##### B.2-1 DrawAutomaton

`‣ DrawAutomaton`( A[, state_names, L] ) | ( function )

This function draws automaton A. The arguments state_names, L and file are optional.

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

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

    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]]);

The output of the three previous `DrawAutomaton` commands would be the following diagrams, respectively.

##### B.2-2 DotForDrawingAutomaton

`‣ DotForDrawingAutomaton`( arg ) | ( function )

This function computes the dot code that can be used to display an automaton. This can be done by using the function `DrawAutomaton` (B.2-1) (if the system is properly configured) or by the user in some independent way. The arguments and options are the same than those of `DrawAutomaton` (B.2-1).

    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"

By using Print (or PrinTo, if one wants to print to a file) the string is displayed as follows:

    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];
    }

The dot code produced for the remaining pictures:

    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];
    }

##### B.2-3 DrawSubAutomaton

`‣ DrawSubAutomaton`( A, B ) | ( function )

This function tests if automaton `A` is a subautomaton of `B` in which case draws `B` highlighting the edges not in `A` by drawing them in a dotted style, while the others are drawn in a plain style.

    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);

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.

##### B.2-4 DotStringForDrawingSubAutomaton

`‣ DotStringForDrawingSubAutomaton`( A, B ) | ( function )

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 `DrawSubAutomaton` (B.2-3) (if the system is properly configured) or can be used by the user in some independent way.

    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"

By using Print (or PrinTo, if one wants to print to a file) the string is displayed as follows:

    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];
    }

##### B.2-5 DotStringForDrawingGraph

`‣ DotStringForDrawingGraph`( G ) | ( function )

`‣ DrawGraph`( G ) | ( function )

Draws a graph specified as an adjacency list `G`.

    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];
    }

The dot code can be used to produce the following picture (which may also be produced by typing `DrawGraph(G);`

##### B.2-6 DrawSCCAutomaton

`‣ DrawSCCAutomaton`( A[, state_names, L] ) | ( function )

Draws automaton `A` and highlights it's strongly connected components by drawing the other edges in a dotted style.

The optional arguments state_names and L are as described in `DrawAutomaton` (B.2-1).

    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];
    }

The dot code can be used to produce the following picture (which may also be produced by typing `DrawGraph(G);`

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