Question

2. If L is a regular language, prove that the language 11 = { uv/ u E 1 , |v|-2) is also regular. (Hint: Can you build an NFA of L1 using an NFA of a language L? Use N, the NFA of the language L)

Answer 1

1)Let's say: Alphabets in the string={a,b}

And regular language be {a^n/n>0}

Therefore u={a^n/n>0}

|v|=2

Therefore v can be {aa,ab,ba,bb}

Since u is regular,v is also regular

we know that UV is also regular because a regular language is closed under concatenation

Therefore it proves that L1 is regular.

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