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### 6. Finite regular languages

This chapter describes some functions to deal with finite regular languages.

#### 6.1 Dealing with finite regular languages

##### 6.1-1 IsFiniteRegularLanguage

`> IsFiniteRegularLanguage`( L ) | ( function )

L is an automaton or a rational expression. This function tests whether its argument represents a finite language or not.

    gap> RandomRatExp(2);
    b*(aU@)
    gap> IsFiniteRegularLanguage(last);
    false
    gap> RandomRatExp(2);
    aUbU@
    gap> IsFiniteRegularLanguage(last);
    true

##### 6.1-2 FiniteRegularLanguageToListOfWords

`> FiniteRegularLanguageToListOfWords`( L ) | ( function )

L is an automaton or a rational expression. This function outputs the recognized language as a list of words.

    gap> r:=RationalExpression("aaUb(aUb)");
    aaUb(aUb)
    gap> FiniteRegularLanguageToListOfWords(r);
    [ "aa", "ba", "bb" ]

##### 6.1-3 ListOfWordsToAutomaton

`> ListOfWordsToAutomaton`( alph, L ) | ( function )

Given an alphabet alph (a list) and a list of words L (a list of lists), outputs an automaton that recognizes the given list of words.

    gap> ListOfWordsToAutomaton("ab",["aaa","bba",""]);
    < deterministic automaton on 2 letters with 6 states >
    gap> FAtoRatExp(last);
    (bbUaa)aU@

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