What is the concatenation of this language with you?

Question

Given the following language:

L1 = { (ab)n | n ≥ 0 }

I.e L1 = { ε ab, abab, ababab, abababab, ... }

The question is to find the language .L12

I assume that it is equal . It's right? If so, how can I prove it? If not, why not?{ (ab)2n | n ≥ 0 }

Thanks!

Answer 1

The language L ₁ ² is the language of all lines of the form xy, where x & in; L ₁ and y & in; L <sub> 1sub>. Note that x and y need not be the same string; they can be selected independently.

, , y = & epsilon;, & epsilon; = (ab) ⁰. L ₁ L ₁ ² & epsilon;.

, , L ₁ ² L ₁. w & in; L < > 1 > ². xy x, y & in; L < > 1 > . , w = xy = (ab) ⁿ (ab) ^m n m. , w = (ab) ^{n + m} w L ₁.

, L ₁ & subseteq; L ₁ ² L ₁ ² & subseteq; L ₁, , L ₁= L ₁ ². , L ₁ ² - , L ₁.

, !