CODEWITHSUNDEEP
regular-language
Happy Mittal
Happy Mittal

Reputation: 3747

Proving a Language to be regular

Pumping Lemma is used to prove a language to be not regular. But How a language can be
proved to be regular ? In particular, 

Let L be a language. Define half(L) to be  
{ x | for some y such that |x| = |y|, xy is in L}.  
Prove for each regular L that half(L) is regular.

Is there any trick or general procedure to tackle such kind of questions ?

Upvotes: 7

Views: 8453

Answers (2)

miku
miku

Reputation: 188014

If you can correctly describe your language L by an NFA or DFA, then it will be regular.

There is a well known equality of NFAs, DFAs, regular grammars and regular expressions, so a representation of L in any of these formalisms should do.

Upvotes: 9

phihag
phihag

Reputation: 287815

Provide a regular grammar or a finite automaton that matches the language. For the full list of properties you can prove to show a language is regular, see the first lines of the Wikipedia Article on regular languages.

Upvotes: 5

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