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<title>GAP (Automata) - Chapter 6: Finite regular languages</title>
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<div class="ChapSects"><a href="chap6.html#X7AF3E5D081126EBD">6 <span class="Heading">Finite regular languages</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X85643AEB7E7FB39A">6.1 <span class="Heading">Dealing with finite regular languages</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X82971FC2851B7B30">6.1-1 IsFiniteRegularLanguage</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7E48CD3E78277FF7">6.1-2 FiniteRegularLanguageToListOfWords</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7F9C5C6F815773E6">6.1-3 ListOfWordsToAutomaton</a></span>
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<h3>6 <span class="Heading">Finite regular languages</span></h3>

<p>This chapter describes some functions to deal with finite regular languages.</p>

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<h4>6.1 <span class="Heading">Dealing with finite regular languages</span></h4>

<p><a id="X82971FC2851B7B30" name="X82971FC2851B7B30"></a></p>

<h5>6.1-1 IsFiniteRegularLanguage</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsFiniteRegularLanguage</code>( <var class="Arg">L</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><var class="Arg">L</var> is an automaton or a rational expression. This function tests whether its argument represents a finite language or not.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">r:=RationalExpression("b*(aU@)");;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">IsFiniteRegularLanguage(last);</span>
false
<span class="GAPprompt">gap></span> <span class="GAPinput">r:=RationalExpression("aUbU@");;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">IsFiniteRegularLanguage(last);</span>
true
</pre></div>

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<h5>6.1-2 FiniteRegularLanguageToListOfWords</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; FiniteRegularLanguageToListOfWords</code>( <var class="Arg">L</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><var class="Arg">L</var> is an automaton or a rational expression. This function outputs the recognized language as a list of words.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">r:=RationalExpression("aaUx(aUb)");   </span>
aaUx(aUb)
<span class="GAPprompt">gap></span> <span class="GAPinput"> FiniteRegularLanguageToListOfWords(r);</span>
[ "aa", "xa", "xb" ]
</pre></div>

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<h5>6.1-3 ListOfWordsToAutomaton</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; ListOfWordsToAutomaton</code>( <var class="Arg">alph</var>, <var class="Arg">L</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Given an alphabet <var class="Arg">alph</var> (a list) and a list of words <var class="Arg">L</var> (a list of lists), outputs an automaton that recognizes the given list of words.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">ListOfWordsToAutomaton("ab",["aaa","bba",""]);</span>
< deterministic automaton on 2 letters with 6 states >
<span class="GAPprompt">gap></span> <span class="GAPinput">FAtoRatExp(last);</span>
(bbUaa)aU@
</pre></div>


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