How is the below language regular ?

Question

If L={a^n w a^n , w={a,b}* }

how come this is a regular language , although I can write like

a(a+b)*a +aa (a+b)*aa but still how are we able to make sure that the power of a from the beginning is the same as the power of from end , plz draw a finite automaton for it , I am stucked up in this .

Answer 1

If $L=\{a^n w a^n , w \in \{a,b\}^* \}$

When a set definition is given, we must consider all possible cases as per the definition- i.e., for a language we must include all possible strings satisfied by the given definition. In this question when we put $n = 0$, we get $L = \Sigma^*$ and that is the maximal set and so we don't need to consider any other value for $n$. And this set is regular. 

Comments

Yes sir , so I guess the DFA would be only one state with a and b move on it and it would be both an initial state and final state ?

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Yes.

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You may look at these.

http://www.gatecse.in/wiki/Identify_the_class_of_the_language