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I still confuse what is a regular language. I read some books, i know if language likes (a^n b^m| n,m>0), it will be regular language since n and m are not related. I know using pumping lemma can prove a language is regular or not, but for this one{a,b}*, i don't know how to do it.

Jason6666
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  • I am afraid you have to go back to your textbooks and read the basics on the topic. The pumping lemma never tells you that a language is regular. It can only tell you that some languages are not regular. Regular languages have closure properties that preserve regularity under some transformation of the language, such as applying the Kleene star operator (Kleene closure). By definition a finite set is regular. The set {a,b}, containing 2 strings of size 1 is therefore regular, and thus its kleene closure {a,b}* is regular too. – babou May 21 '15 at 10:02
  • Thanks sir, but how do you prove a language is regular? – Jason6666 May 21 '15 at 10:17
  • It's a regular language if it's described by a regular expression or accepted by an NFA or DFA (plus a few other characterizations). See our reference questions for more. – David Richerby May 21 '15 at 10:17
  • @babou Thanks! And just in time for me to edit the comment. :-) – David Richerby May 21 '15 at 10:22
  • As you see, there are many ways to make such a proof, that may depend on how the language is initially defined/ described. So you should either read the reference questions or probably preferably spend more time on textbooks. We cannot write anew a full course on the topic just to answer you. What would be the point? – babou May 21 '15 at 10:23
  • @babou Thanks for helping, I will read textbook to understand it. – Jason6666 May 21 '15 at 10:32
  • You should know that a language is regular iff there's a DFA accepting it. Now consider the DFA which has one state which is also an accepting state .. – Elimination May 21 '15 at 10:43

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