When I was TA’ing for Automata Theory, the in-browser finite-state machine creators I found tended to feel either a bit restricted or unable to generate high-quality automata images. Lo and behold, LaTeX already had a package which produced diagrams from a description.

This short guide includes some examples for creating finite state automata using LaTeX and tikz. For something more in-depth, the TikZ and PGF Manual chapter is a great reference.

Finite Automata

tikz is a great package for drawing both deterministic and nondeterministic Finite Automata. The arrows, automata, and positioning libraries used in conjunction provide all we should need.

usepackage{tikz}
usetikzlibrary{arrows,automata,positioning}

Let’s start with four examples that illustrate some of the languages regular languages can represent. The empty set can be recognized by many machines, but the final state is always an empty set.

$$ emptyset = Big( Q = { s_0}, Sigma = { 0, 1}, delta = begin{bmatrix}s_0, s_0end{bmatrix}, q_0 = s_0, F = { } Big) $$

% { }
begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid,auto]
  tikzstyle{every state}=[fill={rgb:black,1;white,10}]

  node[state,initial] (s_0)  {$s_0$};

  path[->]
  (s_0) edge  [loop above]  {0,1} ( );
end{tikzpicture}
  

The natural opposite of a machine that accepts nothing is a machine which accepts everything. By the same logic as before, all automata where Q equals F will recognize this language.

$$ { 0, 1}^* = Big( Q = { s_0 }, Sigma = { 0, 1 }, delta = begin{bmatrix} s_0, s_0 end{bmatrix}, q_0 = s_0, F = { s_0 } Big)$$

% {0,1}*
begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid,auto]
  tikzstyle{every state}=[fill={rgb:black,1;white,10}]

  node[state,initial,accepting] (s_0)  {$s_0$};

  path[->]
  (s_0) edge  [loop above]  {0,1} ( );
end{tikzpicture}
  

Positioning Nodes on the Grid

Now that we’ve seen the two languages which can be expressed with a single state, we turn our focus to those which require two or more states.

The next two languages represent ε and {0,1}+. Respectively these correspond to “the language of strings containing nothing” and “the language of strings containing something”. From these images it is also worth noticing that they are inverses of one another.

These examples use a position parameter to show that s_1 should be positioned to the right of=s_0.

$$ { epsilon } = Big( Q = { s_0, s_1 }, Sigma = { 0, 1