<!-- $Id: finitelang.xml,v 1.12  Exp $ -->

<Chapter><Heading>Finite regular languages</Heading>
This chapter describes some functions to deal with finite regular languages.

<Section><Heading>Dealing with finite regular languages</Heading>

<ManSection> 
<Func Name="IsFiniteRegularLanguage" Arg="L"/>
<Description>
<A>L</A> is an automaton or a rational expression. This function tests
whether its argument represents a finite language or not.
<Example><![CDATA[
gap> RandomRatExp(2);
b*(aU@)
gap> IsFiniteRegularLanguage(last);
false
gap> RandomRatExp(2);
aUbU@
gap> IsFiniteRegularLanguage(last);
true
]]></Example>
</Description> 
</ManSection> 


<ManSection> 
<Func Name="FiniteRegularLanguageToListOfWords" Arg="L"/>
<Description>
<A>L</A> is an automaton or a rational expression. 
This function outputs the recognized language as a list of words.
<Example><![CDATA[
gap> r:=RationalExpression("aaUx(aUb)");   
aaUx(aUb)
gap>  FiniteRegularLanguageToListOfWords(r);
[ "aa", "xa", "xb" ]
]]></Example>
</Description> 
</ManSection> 


<ManSection> 
<Func Name="ListOfWordsToAutomaton" Arg="alph, L"/>
<Description>
Given an alphabet <A>alph</A> (a list) and a list of
words <A>L</A> (a list of lists), outputs an automaton
that recognizes the given list of words.
<Example><![CDATA[
gap> ListOfWordsToAutomaton("ab",["aaa","bba",""]);
< deterministic automaton on 2 letters with 6 states >
gap> FAtoRatExp(last);
(bbUaa)aU@
]]></Example>
</Description> 
</ManSection> 





    </Section>
</Chapter>