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diff --git a/graphics/pgf/base/doc/pgfmanual-en-library-automata.tex b/graphics/pgf/base/doc/pgfmanual-en-library-automata.tex new file mode 100644 index 0000000000..c56bb6fd11 --- /dev/null +++ b/graphics/pgf/base/doc/pgfmanual-en-library-automata.tex @@ -0,0 +1,335 @@ +% 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: |