Question

Test the language L2.16={(ab^n,n>0) with the pumping lemma and show that it is regular.

Answer 1

Let the given language be L. Where L = (abⁿ,n>0) which represents set of all strings where a is followed by 1 or more b's.(at least one b)

So, L can be also represented as, L = (abb*)

Then, let x = uvw be abb and n = 3. Where uv is ab and |ab|<=3.

And |v| >=1.

Now we need to show that if for all i, i>=0, uvⁱw should belongs to L. That is string v has to be pumped, it the language is regular.

So, if i = 0, string we get is {ab} which belongs to L.

if i = 1, string we get is {abb} which belongs to L.

if i = 2, sting we get is {abbb} which belongs to L.

Therefore, so on, for all i, we get all stings belongs to language L only. Since, v is pumped, we can that the given language is regular.