Prove that for each regular language L the following language is
regular:
shift(L) = {uv | vu ∈ L}
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shift(L) = {uv | vu ∈ L}
answer(refer attachment):

Prove that for each regular language L the following language is regular: shift(L) = {uv |...
If L is a regular language, prove that the language {uv : u ∈L, v ∈LR} is also regular
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)
Prove that language L on {a, b}, L={ v | v = vR} is not
regular
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Suppose that L is a regular language. Prove that the language p
r e f i x (L )={w |
x, wx
L } is regular. (For example, if L = {abc, def}, prefix(L) = {?,
a, ab, abc, d, de, def}.)
Prove that, if L is a regular language over the alphabet Σ=(0,1), then L': { ax | x E L } is also regular for any a E Σ
Prove that language L on {a, b}, L={ v | v = vR} is not regular use string ab^nab^na
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Prove that language Lon{a,b}, L={ vv = vR} is not regular.
10. Consider the following CFG: Is the language generated by this CFG a regular language? If so, give a regular expression denoting it. If not, prove it.
10. Consider the following CFG: Is the language generated by this CFG a regular language? If so, give a regular expression denoting it. If not, prove it.