7. The homomorphism h is defined by h(a) = 01 and h(b) = 10. What is h(baba)? a) baba ○ b) 100101 c) 10011001 d) 10101010 8. The operation Perm(w), applied to a string w, is all strings that can be constructed by permuting the symbols of w in any order. For example, if w = 101, then Perm(w) is all strings with two 1's and one 0, i.e., Perm(w) = {101, 110,011}. If L is a regular language, then Perm(L) is the union of Perm(w) taken over all w in L. For example, if L is the language L(0*1*), then Perm(L) is all strings of O's and 1's, i.e., L((0+1)*). If L is regular, Perm(L) is sometimes regular, sometimes context-free but not regular, and sometimes not even context-free. Consider each of the following regular expressions R below, and decide whether Perm(L(R)) is regular, context-free, or neither: 1. (01)* 2.0*+1* 3. (012)* 4. (01+2)* a) Perm(L((01+2)*)) is not context-free. b) Perm(L(0*+1*)) is regular. c) Perm(L((01+2)*)) is regular. d) Perm(L(0*+1*)) is context-free but not regular.

7. The homomorphism h is defined by h(a) = 01 and h(b) = 10. What is h(baba)? a) baba ○ b) 100101 c) 10011001 d) 10101010 8. The operation Perm(w), applied to a string w, is all strings that can be constructed by permuting the symbols of w in any order. For example, if w = 101, then Perm(w) is all strings with two 1's and one 0, i.e., Perm(w) = {101, 110,011}. If L is a regular language, then Perm(L) is the union of Perm(w) taken over all w in L. For example, if L is the language L(01), then Perm(L) is all strings of O's and 1's, i.e., L((0+1)). If L is regular, Perm(L) is sometimes regular, sometimes context-free but not regular, and sometimes not even context-free. Consider each of the following regular expressions R below, and decide whether Perm(L(R)) is regular, context-free, or neither: 1. (01) 2.0+1 3. (012)* 4. (01+2)* a) Perm(L((01+2))) is not context-free. b) Perm(L(0+1)) is regular. c) Perm(L((01+2))) is regular. d) Perm(L(0+1)) is context-free but not regular.