permutation of L

Given a language L, let p(L) be the permutation of L, i.e. the set of
words that are permutations of words in L. For instance, if L = 0*1*,
then p(L) = {0,1}*, and if L = {0^n1^n | n>= 0}, then p(L) contains all
words with equal number of 0's and 1's.

a) Can someone give an example of a regular language L over {0, 1} such
that p(L) is not regular?
b) Prove that if L is a regular language over {0, 1}, then p(L) is a
context-free language.

Any kind of help would be appreciated. Thank you!

.

Relevant Pages

  • Re: More Etymology!
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