Could anyone please help me understand how to answer this question? I know that

Question

Could anyone please help me understand how to answer this question?

I know that for part a ( and correct me if I am wrong): an example of a string accepted in this language would be: aa ab ba bb

because u = Sigma^2={(aa),(ab),(ba),(bb)}

and an example of a string not in the language would be: a

but I don't understand the other parts.

Let = {a, 6}. For each of the languages below, give an example of a string in the language, and a string not in the language. {w : w = uuRu. for some u } {w : ww = www] {w : uvw = wvu. for some u, v } {w : www = uu, for some u }.

Explanation / Answer

Answer you have given for (a) is correct.

(b) Example of a string that is in the language : w = epsilon (null)

then www = ww

Example of a string that is not in the language : w = a

aaa != aa

(c) Example of a string that is in the language : u = a, v = epsilon, w = a

uvw = a(epsilon)a = aa

wvu = a(epsilon)a = aa

Example of a string that is not in the language : u = a, v = epsilon, w = b

uvw = a(epsilon)b = ab

wvu = b(epsilon)a = ba

(c) Example of a string that is in the language : w = abab, u = ababab

uu = (ababab)(ababab) = abababababab

www = (abab)(abab)(abab) = abababababab

Example of a string that is not in the language : u = a,w = b

www = bbb

uu = aa

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