# russross/automata

Automata (DFA/NFA/PDA/TM) diagrams made easy with LaTeX and Metapost
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figure-examples.tex
theory.mp

# Automata diagrams for LaTeX

I wrote these macros to make it easier to create diagrams of finite automata (DFAs and NFAs), pushdown automata (PDAs), Turing machines, etc. I use LaTeX to prepare my slides and problem sets, and I require my students to use LaTeX in writing up their solutions. This package makes it simple to create figures using Metapost that can easily be included in LaTeX documents of all types.

To get started, look at figure-examples.tex, which contains a few basic examples. For those conversent with LaTeX and Metapost, the macros are based around the Metapost boxes package. Simple wrappers make it easier to create nodes with consistent sizing and to mark start and accept nodes.

The edge command makes it easy to draw straight and curved edges between nodes. It also places labels intelligently, halfway between the end nodes and adjusted so that larger labels do not overlap the edge.

## Inline figures

The example .tex file also shows how to use the emp LaTeX package, which makes it convenient to write your figures inline with the rest of the LaTeX code.

In the prelude of your LaTeX document, include a few packages:

\usepackage{emp,ifpdf}
\usepackage{graphicx}


Metapost produces embedded postscript, but it happens to also be valid PDF code, so we instruct LaTeX to do the conversion automatically (the result will work with pdflatex or regular latex):

\ifpdf\DeclareGraphicsRule{*}{mps}{*}{}\fi


To include the macros and the boxes package that they depend on, have LaTeX put a header in the Metapost file it produces:

\empprelude{input boxes; input theory}


Next, inside the document itself start a Metapost file:

\begin{empfile}


At the end of the document (any time after the last figure) close it with:

\end{empfile}


Each time you want to create a figure, do so in an emp environment:

\begin{emp}(0,0)
% figure goes here
\end{emp}


I usually center my figures by nesting them in a center environment.

Where I've put (0,0), you can specify the size of the figure. All it does is define variables w and h with the width and height, respectively. You can use those in your figure definition to make a scalable figure. I don't usually bother, so I just declare each one with (0,0).

One caveat: the emp environment uses verbatim, which makes this fail in some circumstances. Notably, if you use the beamer package for preparing slides, you will need to start the frame with:

\begin{frame}[containsverbatim]{Title of slide}


or it will fail with mysterious error messages.

You can also define a named figure and include it later. Only the definition uses a verbatim environment, so you can include the figure itself anywhere, including as a parameter to a macro. To do so, define the figure in an empdef environment:

\begin{empdef}[figurename](0,0)
% figure goes here
\end{empdef}


Then when you want to include it, use:

\empuse{figurename}


One more hint: when including small figures inline with text, it is often nice to be able to shift it up or down a bit to line it up with the text. To do that, create a named figure, then use something like: \raisebox{.25em}{\empuse{figurename}}

When compiling the LaTeX file, you must instruct it to permit external programs to be run:

pdflatex -shell-escape myfile.tex


You also need to run the command twice. The first time dumps the figures into a file and runs Metapost on it, the second time actually includes the rendered figures.

## Tutorial

Inside each figure, I usually define a size unit and specify all spacing in terms of that unit:

u := 1cm;


Then I can tweak the size easily. This does not scale the size of nodes, tape squares, or labels, but it is helpful even so.

### Nodes

To create a DFA node, use the node macro:

node.q0("label");


This creates a node with the internal name q0, and displays the given label inside it when rendered. The label can be omitted.

The label can be a simple string, or you can render something using LaTeX:

node.q0(btex $a$ etex);


I have defined a bunch of common labels already, which can be used as node labels, edge labels, or anywhere else. This example could have been written:

node.q0(A);


Here is the complete list of pre-defined labels:

A, B, AB, C, E, K, N, X, Y, Z, ZERO, ONE, ZEROONE, SIGMA,
EMPTYSET, CDOTS, VDOTS, SQCUP, BLANK


If you are unsure about what any of them are, look at theory.mp for the definitions or try them out.

Nodes use the Metapost boxes package. It provides anchor points at the center, north, south, each, and west points on the node, accessible as q0.c, q0.n, q0.e, etc. You must specify one such point for each node, and the rest will be computed automatically:

q0.c = (0,0);


You can anchor additional nodes using absolute positioning, or you can place them relative to each other:

node.q1();
q1.c = q0.c + (2u,0);


Up to this point, nothing will actually be displayed. The basic rule is that Metapost must be able to compute absolute positions for each object before it can be rendered. When you have given it enough information to do so, you can draw one or more nodes using the drawboxed command:

drawboxed(q0,q1);


This draws the nodes and their labels. If you only want the nodes (without labels), use:

drawboxes(q0,q1);


And if you only want labels but no boxes, use:

drawunboxed(q0,q1);


This is occasionally useful if you want to use different colors, for example.

### Start and final nodes

Final nodes are displayed with a smaller circle inside the main node. To mark nodes as final nodes, use:

makefinal(q0,q1);


This draws the line immediately, so you cannot use it until the node's position has been established. Similarly, you can mark nodes as start nodes:

makestart(q0,q1);


This draws a > sign on the left of the node. To put it on the top instead, use:

makestart_top(q0,q1);


### Edges

Next are edges. Edges can be defined in several ways. A simple straight edge with no label from q0 to q1:

sedge(q0,q1);


Edges are directed by default, but you can specify undirected edges as well. The general form of edges is this:

edge(from,to,angle,label);


from and to are nodes. angle can be "left" or "right" to specify a straight edge (with the label on the left or right, respectively), "curve" to indicate a default curve, "-curve" to curve the other way, or any angle (in degrees) that you specify. When you specify an angle, you are instructing it to set the angle (relative to a straight edge) at the point the edge leaves the start node and arrives at the destination node.

If you don't want a label, use BLANK as the label. A few examples:

% a straight, empty transition (labeled with \varepsilon) with
% the label on the left side
edge(q0,q1,left,E);

% a curved edge with $a$ as the label
edge(q0,q1,curve,A);

% a -45 degree curve (negative angles curve right)
edge(q0,q1,-45,B);

% a right-curved edge with no label
edge(q0,q1,-curve,BLANK);


Edges are rendered immediately, so both end nodes must be positioned.

The edge macro tries to place the label in a good place. It starts by placing it at the center of the edge on the outside of the curve (or on the side you specify for straight edges). Then it starts nudging it further out until the bounding box of the label no longer overlaps the edge. The direction it nudges it is chosen based on the shape of the label. It tends to give a good result even for long or tall labels. It only worries about the edge, however; you must provide enough space to prevent overlap with nodes.

### Loops

Looped edges are a special case. You must specify the node, the side of the node the loop should be attached to (up, down, left, or right), and the label:

loop(q0,up,AB);


### Node sizes

A series of node sizes are predefined. Declare the size you want before you start making nodes. From largest to smallest:

hugenodes;
bignodes;
mediumnodes;
smallnodes;
tinynodes;
mininodes;


Note that changes in one figure persist to the next if you use multiple figures in one file, so it is best to explicitly select a size in each figure.

### Edge colors

You can change edge colors using:

rededges;
blueedges;
greenedges;
blackedges;


or you can assign a Metapost color to edgecolor.

### Other options

Similarly, you can turn dashed edges on and off using:

dashededges;
solidedges;


And for directed and undirected edges:

directededges;
undirectededges;


Note that these only affect edges. If you want colored or dashed nodes, use the metapost command:

drawoptions(withcolor blue);
drawoptions(dashed evenly);
drawoptions(dashed evenly withcolor blue);


To reset such options, use the command with no options:

drawoptions();


These commands affect all drawing, not just nodes.

### Tape squares

To draw tapesquares, first declare that you are beginning a tape:

begintape;


Or for a vertical tape (a stack):

beginverticaltape;


In either case, create a series of squares as you would nodes:

tapesquare.a(A);
tapesquare.b(B);
tapesquare.c(X);


You must anchor a single point on any one of the squares; all of the rest will be positioned automatically. In addition to the points you can use with nodes, you can use nw, ne, sw, and se to specify the four corners of each square.

The sizes of the squares are set according to the label BIGGEST, which defaults to be the same as B. Each square will be big enough to accommodate the longest dimension of BIGGEST. If you are using custom labels, you may need to reset BIGGEST to match your largest label (before creating any tape squares):

BIGGEST := AB;


If you want an open-ended square at the end of the tape, use:

tapecontinueright(rightmostsquare);


or at the left end of the tape:

tapecontinueleft(leftmostsquare);


To mark the bottom of a stack with lines sticking out, use:

stackbottom(bottomsquare);


Note that these do not actually create tape nodes, but rather decorate existing nodes. The label and lines are rendered immediately, so the tape square must be positioned already. For the actual tape squares, you must use drawboxed() and its kin to display the tape squares, just as you would with nodes.

When you reach the end of the tape (either kind), mark it with:

endtape;


A simple macro is included for drawing normal Metapost arrows that are shortened a bit at both ends:

shortarrow(startpoint,endpoint,2pt);


This would draw an arrow from the start point to the end, but shortened by 2 points. Note that these are points, not nodes.

Finally, another convenience macro to draw a box by specifying the left, right, top, and bottom coordinates:

drawbox(0,2u,5u,4u);


For more information about Metapost in general, various references and tutorials are available online. These macros are enough for most basic diagrams my students need to create, but Metapost is capable of a lot more.

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