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+% Copyright 2019 by Till Tantau
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Free Documentation License.
+%
+% See the file doc/generic/pgf/licenses/LICENSE for more details.
+
+
+\section{Automata Drawing Library}
+
+\begin{tikzlibrary}{automata}
+ This packages provides shapes and styles for drawing finite state automata
+ and Turing machines.
+\end{tikzlibrary}
+
+
+\subsection{Drawing Automata}
+
+The |automata| (drawing) library is intended to make it easy to draw finite
+automata and Turing machines. It does not cover every situation imaginable, but
+most finite automata and Turing machines found in text books can be drawn in a
+nice and convenient fashion using this library.
+
+To draw an automaton, proceed as follows:
+%
+\begin{enumerate}
+ \item For each state of the automaton, there should be one node with the
+ option |state|.
+ \item To place the states, you can either use absolute positions or
+ relative positions, using options like |above| or |right|.
+ \item Give a unique name to each state node.
+ \item Accepting and initial states are indicated by adding the options
+ |accepting| and |initial|, respectively, to the state nodes.
+ \item Once the states are fixed, the edges can be added. For this, the
+ |edge| operation is most useful. It is, however, also possible to add
+ edges after each node has been placed.
+ \item For loops, use the |edge [loop]| operation.
+\end{enumerate}
+
+Let us now see how this works for a real example. Let us consider a
+nondeterministic four state automaton that checks whether an input contains the
+sequence $0^*1$ or the sequence $1^*0$.
+%
+\begin{codeexample}[preamble={\usetikzlibrary{automata,positioning}}]
+\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid,auto]
+ \draw[help lines] (0,0) grid (3,2);
+
+ \node[state,initial] (q_0) {$q_0$};
+ \node[state] (q_1) [above right=of q_0] {$q_1$};
+ \node[state] (q_2) [below right=of q_0] {$q_2$};
+ \node[state,accepting](q_3) [below right=of q_1] {$q_3$};
+
+ \path[->] (q_0) edge node {0} (q_1)
+ edge node [swap] {1} (q_2)
+ (q_1) edge node {1} (q_3)
+ edge [loop above] node {0} ()
+ (q_2) edge node [swap] {0} (q_3)
+ edge [loop below] node {1} ();
+\end{tikzpicture}
+\end{codeexample}
+
+
+\subsection{States With and Without Output}
+
+The |state| style actually just ``selects'' a default underlying style. Thus,
+you can define multiple new complicated state style and then simply set the
+|state| style to your given style to get the desired kind of styles.
+
+By default, the following state styles are defined:
+%
+\begin{stylekey}{/tikz/state without output}
+ This node style causes nodes to be drawn as circles. Also, this style calls
+ |every state|.
+\end{stylekey}
+
+\begin{stylekey}{/tikz/state with output}
+ This node style causes nodes to be drawn as split circles, that is, using
+ the |circle split| shape. In the upper part of the shape you have the name
+ of the style, in the lower part the output is placed. To specify the
+ output, use the command |\nodepart{lower}| inside the node. This style also
+ calls |every state|.
+ %
+\begin{codeexample}[preamble={\usetikzlibrary{automata}}]
+\begin{tikzpicture}
+ \draw[help lines] (0,0) grid (3,2);
+
+ \node[state without output] {$q_0$};
+
+ \node[state with output] at (2,0) {$q_1$ \nodepart{lower} $00$};
+\end{tikzpicture}
+\end{codeexample}
+ %
+\end{stylekey}
+
+\begin{stylekey}{/tikz/state (initially state without output)}
+ You should redefine it to something else, if you wish to use states of a
+ different nature.
+ %
+\begin{codeexample}[preamble={\usetikzlibrary{automata}}]
+\begin{tikzpicture}[state/.style=state with output]
+ \node[state] {$q_0$ \nodepart{lower} $11$};
+ \node[state] at (2,0) {$q_1$ \nodepart{lower} $00$};
+\end{tikzpicture}
+\end{codeexample}
+ %
+\end{stylekey}
+
+\begin{stylekey}{/tikz/every state (initially \normalfont empty)}
+ This style is used by |state with output| and also by
+ |state without output|. By default, it does nothing, but you can use it to
+ make your state look more fancy:
+ %
+\begin{codeexample}[preamble={\usetikzlibrary{arrows.meta,automata,positioning}}]
+\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid,>={Stealth[round]},
+ every state/.style={draw=blue!50,very thick,fill=blue!20}]
+
+ \node[state,initial] (q_0) {$q_0$};
+ \node[state] (q_1) [above right=of q_0] {$q_1$};
+ \node[state] (q_2) [below right=of q_0] {$q_2$};
+
+ \path[->] (q_0) edge node [above left] {0} (q_1)
+ edge node [below left] {1} (q_2)
+ (q_1) edge [loop above] node {0} ()
+ (q_2) edge [loop below] node {1} ();
+\end{tikzpicture}
+\end{codeexample}
+ %
+\end{stylekey}
+
+
+\subsection{Initial and Accepting States}
+
+The styles |initial| and |accepting| are similar to the |state| style as they
+also just select an ``underlying'' style, which installs the actual settings
+for initial and accepting states.
+
+Let us start with the initial states.
+%
+\begin{stylekey}{/tikz/initial (initially initial by arrow)}
+ This style is used to draw initial states.
+\end{stylekey}
+
+\begin{stylekey}{/tikz/initial by arrow}
+ This style causes an arrow and, possibly, some text to be added to the
+ node. The arrow points from the text to the node. The node text and the
+ direction and the distance can be set using the following key:
+ %
+ \begin{key}{/tikz/initial text=\meta{text} (initially start)}
+ This key sets the text to be used. Use an empty text to suppress all
+ text.
+ \end{key}
+ %
+ \begin{key}{/tikz/initial where=\meta{direction} (initially left)}
+ Set the place where the text should be shown. Allowed values are
+ |above|, |below|, |left|, and |right|.
+ \end{key}
+ %
+ \begin{key}{/tikz/initial distance=\meta{distance} (initially 3ex)}
+ Sets the length of the arrow leading from the text to the state node.
+ \end{key}
+ %
+ \begin{stylekey}{/tikz/every initial by arrow (initially \normalfont empty)}
+ This style is executed at the beginning of every path that contains the
+ arrow and the text. You can use it to, say, make the text red or
+ whatever.
+ \end{stylekey}
+ %
+\begin{codeexample}[preamble={\usetikzlibrary{automata}}]
+\begin{tikzpicture}[every initial by arrow/.style={text=red,->>}]
+ \node[state,initial,initial distance=2cm] {$q_0$};
+\end{tikzpicture}
+\end{codeexample}
+ %
+\end{stylekey}
+
+\begin{stylekey}{/tikz/initial above}
+ This is a shorthand for |initial by arrow,initial where=above|.
+\end{stylekey}
+
+\begin{stylekey}{/tikz/initial below}
+ Works similarly to the previous option.
+\end{stylekey}
+
+\begin{stylekey}{/tikz/initial left}
+ Works similarly to the previous option.
+\end{stylekey}
+
+\begin{stylekey}{/tikz/initial right}
+ Works similarly to the previous option.
+\end{stylekey}
+
+\begin{stylekey}{/tikz/initial by diamond}
+ This style uses a diamond to indicate an initial node.
+\end{stylekey}
+
+For the accepting states, the situation is similar: There is also an
+|accepting| style that selects the way accepting states are rendered. There are
+now two options: First, |accepting by arrow|, which works the same way as
+|initial by arrow|, only with the direction of arrow reversed, and
+|accepting by double|, where accepting states get a double line around them.
+
+\begin{stylekey}{/tikz/accepting (initially accepting by double)}
+ This style is used to draw accepting states. You can replace this by the
+ style |accepting by arrow| to get accepting states with an arrow leaving
+ them.
+\end{stylekey}
+
+\begin{stylekey}{/tikz/accepting by double}
+ This style causes a double line to be drawn around a state.
+\end{stylekey}
+
+\begin{stylekey}{/tikz/accepting by arrow}
+ This style causes an arrow and, possibly, some text to be added to the
+ node. The arrow points to the text from the node.
+
+ The same options as for initial states can be used, only with |initial|
+ replaced by |accepting|:
+ %
+ \begin{key}{/tikz/accepting text=\meta{text} (initially \normalfont empty)}
+ This key sets the text to be used.
+ \end{key}
+ %
+ \begin{key}{/tikz/accepting where=\meta{direction} (initially right)}
+ Set the place where the text should be shown. Allowed values are
+ |above|, |below|, |left|, and |right|.
+ \end{key}
+ %
+ \begin{key}{/tikz/initial distance=\meta{distance} (initially 3ex)}
+ Sets the length of the arrow leading from the text to the state
+ node.
+ \end{key}
+ %
+ \begin{stylekey}{/tikz/every accepting by arrow (initially \normalfont empty)}
+ Executed at the beginning of every path that contains the arrow and the
+ text.
+ \end{stylekey}
+ %
+\begin{codeexample}[preamble={\usetikzlibrary{arrows.meta,automata,positioning}}]
+\begin{tikzpicture}
+ [shorten >=1pt,node distance=2cm,on grid,>={Stealth[round]},initial text=,
+ every state/.style={draw=blue!50,very thick,fill=blue!20},
+ accepting/.style=accepting by arrow]
+
+ \node[state,initial] (q_0) {$q_0$};
+ \node[state] (q_1) [above right=of q_0] {$q_1$};
+ \node[state] (q_2) [below right=of q_0] {$q_2$};
+ \node[state,accepting](q_3) [below right=of q_1] {$q_3$};
+
+ \path[->] (q_0) edge node [above left] {0} (q_1)
+ edge node [below left] {1} (q_2)
+ (q_1) edge node [above right] {1} (q_3)
+ edge [loop above] node {0} ()
+ (q_2) edge node [below right] {0} (q_3)
+ edge [loop below] node {1} ();
+\end{tikzpicture}
+\end{codeexample}
+ %
+\end{stylekey}
+
+\begin{stylekey}{/tikz/accepting above}
+ This is a shorthand for |accepting by arrow,accepting where=above|.
+\end{stylekey}
+
+\begin{stylekey}{/tikz/accepting below}
+ Works similarly to the previous option.
+\end{stylekey}
+
+\begin{stylekey}{/tikz/accepting left}
+ Works similarly to the previous option.
+\end{stylekey}
+
+\begin{stylekey}{/tikz/accepting right}
+ Works similarly to the previous option.
+\end{stylekey}
+
+
+\subsection{Examples}
+
+In the following example, we once more typeset the automaton presented in the
+previous sections. This time, we use the following rule for accepting/initial
+state: Initial states are red, accepting states are green, and normal states
+are orange. Then, we must find a path from a red state to a green state.
+%
+\begin{codeexample}[preamble={\usetikzlibrary{arrows.meta,automata,positioning,shadows}}]
+\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid,>={Stealth[round]},thick,
+ every state/.style={fill,draw=none,orange,text=white,circular drop shadow},
+ accepting/.style ={green!50!black,text=white},
+ initial/.style ={red,text=white}]
+
+ \node[state,initial] (q_0) {$q_0$};
+ \node[state] (q_1) [above right=of q_0] {$q_1$};
+ \node[state] (q_2) [below right=of q_0] {$q_2$};
+ \node[state,accepting](q_3) [below right=of q_1] {$q_3$};
+
+ \path[->] (q_0) edge node [above left] {0} (q_1)
+ edge node [below left] {1} (q_2)
+ (q_1) edge node [above right] {1} (q_3)
+ edge [loop above] node {0} ()
+ (q_2) edge node [below right] {0} (q_3)
+ edge [loop below] node {1} ();
+\end{tikzpicture}
+\end{codeexample}
+
+The next example is the current candidate for the five-state busiest beaver:
+%
+\begin{codeexample}[preamble={\usetikzlibrary{arrows.meta,automata,positioning}}]
+\begin{tikzpicture}[->,>={Stealth[round]},shorten >=1pt,%
+ auto,node distance=2cm,on grid,semithick,
+ inner sep=2pt,bend angle=45]
+ \node[initial,state] (A) {$q_a$};
+ \node[state] (B) [above right=of A] {$q_b$};
+ \node[state] (D) [below right=of A] {$q_d$};
+ \node[state] (C) [below right=of B] {$q_c$};
+ \node[state] (E) [below=of D] {$q_e$};
+
+ \path [every node/.style={font=\footnotesize}]
+ (A) edge node {0,1,L} (B)
+ edge node {1,1,R} (C)
+ (B) edge [loop above] node {1,1,L} (B)
+ edge node {0,1,L} (C)
+ (C) edge node {0,1,L} (D)
+ edge [bend left] node {1,0,R} (E)
+ (D) edge [loop below] node {1,1,R} (D)
+ edge node {0,1,R} (A)
+ (E) edge [bend left] node {1,0,R} (A);
+\end{tikzpicture}
+\end{codeexample}
+
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "pgfmanual-pdftex-version"
+%%% End: