<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
 "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">

<head>

<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>groupuniv-source</title>

<link rel="stylesheet" href="../../style.css" type="text/css" />

<link rel="stylesheet" href="../../local.css" type="text/css" />




<link rel="alternate" type="application/x-wiki" title="Edit this page" href="/ikiwiki.cgi?page=Vaucanson-G%2Fgroupuniv-source&amp;do=edit" />







</head>
<body>

<div class="page">

<div class="pageheader">
<div class="header">
<span>
<span class="parentlinks">

<a href="../../">The Vaucanson Project</a>/ 

<a href="../">Vaucanson-G</a>/ 

</span>
<span class="title">
groupuniv-source

</span>
</span>



</div>







</div>



<div class="sidebar">
<h3><a href="../../Vaucanson/">Vaucanson</a></h3>

<h3><a href="../">Vaucanson-G</a></h3>

<ul>
<li><p><a href="../Examples/">Examples</a></p></li>
<li><p><a href="../FAQ/">FAQ</a></p></li>
</ul>


<h3>Past projects</h3>

<ul>
<li><p><a href="../../VGI/">VGI</a></p></li>
<li><p><a href="../../FSM-XML/">FSM-XML</a></p></li>
</ul>


<h3><a href="../../Index/">All pages</a></h3>

</div>



<div id="pagebody">

<div id="content">
<pre><code>%---&gt; 26 states
%---&gt; universel automaton of a ``pure-group'' language
\begin{VCPicture}{(-7,-11)(7,10)}
\PlainState
%
\StateIF[p]{(-1,7)}{P}   \StateIF[s]{(1,7)}{S}
\State[q]{(-4.46,8)}{Q}  \StateIF[t]{(4.46,8)}{T}
\State[r]{(-4.46,6)}{R}  \StateIF[u]{(4.46,6)}{U}
%
\StateIF[pq]{(-4,-2)}{PQ}  \StateIF[st]{(4,2)}{ST}
\State[qr]{(-2,0)}{QR}     \StateIF[tu]{(2,0)}{TU}
\StateIF[pr]{(-4,2)}{PR}   \StateIF[su]{(4,-2)}{SU}
\StateIF[pt]{(2,4)}{PT}    \StateIF[pu]{(2,-4)}{PU}
\State[qu]{(0,2)}{QU}      \State[qs]{(-2,-4)}{QS}
\State[rs]{(-2,4)}{RS}     \State[rt]{(0,-2)}{RT}
%
\ChgStateLabelScale{1.3}
\LargeState
\StateIFX[pqr]{(-6,-6)}{PQR}  \StateIF[ptu]{(4,-8)}{PTU}
\StateIF[pqu]{(-2,-7)}{PQU}   \State[qsu]{(2,-7)}{QSU}
\State[qrs]{(-4,-8)}{QRS}     \State[rst]{(2,-9)}{RST}
\StateIF[prt]{(-2,-9)}{PRT}   \StateIFX[stu]{(6,-6)}{STU}
%
\FixDimEdge{dotted}{.5}{gray}{gray}
\DimEdge
\EdgeL{P}{PQ}{} \EdgeL{P}{PR}{} \EdgeL{P}{PT}{} \EdgeL{P}{PU}{}
\EdgeL{Q}{PQ}{} \EdgeL{Q}{QR}{} \EdgeL{Q}{QS}{} \EdgeL{Q}{QU}{}
\EdgeL{R}{PR}{} \EdgeL{R}{QR}{} \EdgeL{R}{RS}{} \EdgeL{R}{RT}{}
\EdgeL{S}{QS}{} \EdgeL{S}{RS}{} \EdgeL{S}{ST}{} \EdgeL{S}{SU}{}
\EdgeL{T}{PT}{} \EdgeL{T}{RT}{} \EdgeL{T}{ST}{} \EdgeL{T}{TU}{}
\EdgeL{U}{PU}{} \EdgeL{U}{QU}{} \EdgeL{U}{SU}{} \EdgeL{U}{TU}{}
%
\EdgeL{PQ}{PQR}{} \EdgeL{QR}{PQR}{} \EdgeL{PR}{PQR}{}
\EdgeL{QR}{QRS}{} \EdgeL{QS}{QRS}{} \EdgeL{RS}{QRS}{}
\EdgeL{PR}{PRT}{} \EdgeL{PT}{PRT}{} \EdgeL{RT}{PRT}{}
\EdgeL{PQ}{PQU}{} \EdgeL{PU}{PQU}{} \EdgeL{QU}{PQU}{}
\EdgeL{ST}{STU}{} \EdgeL{SU}{STU}{} \EdgeL{TU}{STU}{}
\EdgeL{PT}{PTU}{} \EdgeL{PU}{PTU}{} \EdgeL{TU}{PTU}{}
\EdgeL{QS}{QSU}{} \EdgeL{QU}{QSU}{} \EdgeL{SU}{QSU}{}
\EdgeL{RS}{RST}{} \EdgeL{RT}{RST}{} \EdgeL{ST}{RST}{}
\RstEdge
%
\Initial[s]{P} \Final[n]{T} \Final[s]{S} \Final[s]{U}
%
\Initial{PQ} \Initial{PR} \Initial[s]{PT} \Initial[n]{PU}
\Final{ST} \Final[e]{TU} \Final{SU}
%
\Initial[sw]{PQR} \Initial[n]{PQU} \Initial[s]{PRT}
\Initial[s]{PTU} \Final[se]{STU}
%
\EdgeR{P}{Q}{a}   \LoopW{Q}{b}
\ArcR{Q}{R}{a}    \LoopW{R}{b}
\EdgeR{R}{P}{a}   \LoopE{T}{b}
\EdgeL{S}{T}{a}   \LoopE{U}{b}
\ArcL{T}{U}{a}    \ArcL{P}{S}{b}
\EdgeL{U}{S}{a}   \ArcL{S}{P}{b}
%
\EdgeR{PQ}{QR}{a}  \EdgeL{PT}{QU}{a}
\EdgeR{QR}{PR}{a}  \EdgeL{QU}{RS}{a}
\EdgeR{PR}{PQ}{a}  \EdgeL{RS}{PT}{a}
%
\EdgeL{PU}{QS}{a}  \EdgeR{SU}{ST}{a}
\EdgeL{QS}{RT}{a}  \EdgeR{ST}{TU}{a}
\EdgeL{RT}{PU}{a}  \EdgeR{TU}{SU}{a}
%
\LoopE[.8]{QR}{b}
\LoopW[.2]{TU}{b}
\LoopN[.8]{RT}{b}
\LoopS[.2]{QU}{b}
%
\ArcL{PQ}{QS}{b}  \ArcL{ST}{PT}{b}
\ArcL{QS}{PQ}{b}  \ArcL{PT}{ST}{b}
\ArcL{PU}{SU}{b}  \ArcL{RS}{PR}{b}
\ArcL{SU}{PU}{b}  \ArcL{PR}{RS}{b}
%
\EdgeR{PQU}{QRS}{a}  \EdgeR{QSU}{RST}{a}
\EdgeR{QRS}{PRT}{a}  \EdgeR{RST}{PTU}{a}
\EdgeR{PRT}{PQU}{a}  \EdgeR{PTU}{QSU}{a}
%
\LoopL{135}{PQR}{a}  \LoopL{45}{STU}{a}
%
\ArcL{QRS}{PQR}{b}  \ArcL{PQU}{QSU}{b}
\ArcL{PQR}{QRS}{b}  \ArcL{QSU}{PQU}{b}
\ArcL{PTU}{STU}{b}  \ArcL{PRT}{RST}{b}
\ArcL{STU}{PTU}{b}  \ArcL{RST}{PRT}{b}
\end{VCPicture}
</code></pre>

</div>







</div>

<div id="footer" class="pagefooter">

<div id="pageinfo">






<div id="backlinks">
Links:

<a href="../Examples/">Examples</a>


</div>



<div class="actions">
<ul>

<li><a href="/ikiwiki.cgi?page=Vaucanson-G%2Fgroupuniv-source&amp;do=edit" rel="nofollow">Edit</a></li>


<li><a href="../../recentchanges/">RecentChanges</a></li>




<li><a href="/ikiwiki.cgi?do=prefs">Preferences</a></li>





</ul>
</div>






<div class="pagedate">
Last edited <span class="date">Tue 06 May 2014 17:16:00 BST</span>
<!-- Created <span class="date">Tue 06 May 2014 17:16:00 BST</span> -->
</div>

</div>


<!-- from The Vaucanson Project -->
</div>

</div>

</body>
</html>
