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1.1 Let L = {aa, c, bab}. Which of the following strings is in L*? a. aacca b. cbababc c. caaaac d. babcac 1.2 Consider the following grammar:

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1.1 Let L = {aa, c, bab}. Which of the following strings is in L*? a. aacca b. cbababc c. caaaac d. babcac 1.2 Consider the following grammar: S->xAxI yBy A -> λIwB B -> zA Which of the following sentences can be derived from this grammar? a. xwzx b. xxwz c. yywz d. yzwy 3.1 Which of the following is a regular expression for L = a n b m : n, m >=3} a. a*b* b. aaabbb c. aaaa*bbbb* d. b*b*b*a*a*a* 3.2 Find a nfa that accepts L((a+b) (cc+dd)*e) 4.1 Suppose L 1 = L(ab*c* + ccbba), and L 2 = L(c*b*a + abbcc). What is L1 ∩ L2? a. L(a*b*c*) b. L(ab*c + c*b*a)
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c. L(a + ccbba + abbcc) d. L(abc) 4.2 Prove, using the pumping lemma, that the following language for Ʃ = {a. b, c} os mpt regular: L = {w: n a (w) >n b (w)>n c (w)} 5.1 Show that the following grammar is ambiguous: S -> BC I BD S -> a I ab C -> bc I d D -> c I cd 7.1 Construct a npda to accept the language of the following grammar: S -> aB I bA A -> bBB I c B -> aAA I c 8.1 Consider L 1 = {a n b m c m d n : m,n >=0} and L 2 = {a n b m c n d m : m, n>=0}. L 1 is context-free, but L 2 is not. Give a intuitive explanation as to why. (Note: You do not need to use the pumping lemma on L 2 )
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