Given are 2 different languages and I'd like to know if I understand them correctly.
L ⊆ ∑* is a regular language.
cycle(L) = {vu ∈ ∑* | uv ∈ L}
L/2 = {x ∈ ∑* | ∃y ∈ ∑* : xy ∈ L, |x| = |y|}
I need to know that because the actual task is to show that these languages are regular by either describing how you build a DFA or NFA for them.
But I just like to know if I understood them correctly.
So 1. means that every word has an existing reverse.
As example we have word aaa
and bab
, if we concatenate them, we have aaabab
. Now the language says that there is also a word babaaa
- Means that we have two words of same length and we concatenate them?