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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("aaUx(aUb)");
aaUx(aUb)
gap>  FiniteRegularLanguageToListOfWords(r);
[ "aa", "xa", "xb" ]
```

##### 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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