Q39 show that the regular languages are closed under

Q39. Show that the regular languages are closed under the following operation-
max (L) = {w/ w is in L for no x other than € is wx is in L}.
Q40. What is Pumping lemma and what is the closure property of regular set. Prove that
q
1
0
q2
q3
1

regular sets are closed under union, concatenation and Kleen closure.
Q41. Find out whether these two F.A’s are equivalent or not-
i)
0 1
1 0
1 1
ii)
0,1 1
Module-4:
Q42. What is the concept of parse tree in context free grammar? What is parser? How to
remove the ambiguities from the grammar. What is inherent ambiguity explain.
Q43. Define deviation tree. Find deviation tree a * b+ a*b given that-
a*b +a* b is in L(G), where G is given by S→S+S /SS /a /b.
Q44. Construed the context free grammar to generate the corresponding language-
(a) { 0 m 1 m / 1≤ m ≤n}
(b) {a l b m c n / l + m =n}.
Q45. Consider the following production: S-aB /bA.
1) leftmost derivation
2) rightmost derivation
3) parse tree.
Q46. Show that i) S-aB/ab, A-aAB/a, B-ABb/b
ii)S-S+S/ S*S/ a/b
iii) S-aS/X, X-aX/a is ambiguous.
Q47.The following grammar generate regular expression with operand X and Y and binary operator. +, -,
And *.
E→ +EE/ *EE / -EE /x /y.
(a) Find leftmost and rightmost deviation, and deviation tree for the string +* - xyxy.
(b) Prove that this grammar is unambiguous.
Q48. Set of all strings of balanced parenthesis i.e. each left parenthesis has a mattering right parenthesis
and a pairs if matching parenthesis are properly nested.
Q49. Proof –it is an unambiguous grammar-
S-0A/0B
q0
q1
q
3
0,
1
q2
q
4
q5
0
0,
1
0
q'0 q'1
0,
1
0
q'
2

A-1A/€
B-0B/1
Q50. RE (001+1)*(01)*obtain the contex free grammar.
Q51. Obtain the grammar to generate language –
L={ w/ n
a
(w)=n
b
(w)}
Q52. Obtain a grammar to generate the language-
L={ww R /w є {a,b}*
Q53. Obtain a grammar to generate the language-
L= {0 i 1 j /i ≠ j, i≥0 and j≥0}.
Q54. Construct grammar generating {xx/x є {a,b}*}
Q55. Construct grammar generating {0
n
1
2n
/ n≥ 1}.
Q56. Construct grammar generating {a
i
b
j
c
k
/ i, j, k ≥1, i≠j=k}
Q57. Consider CFG G defines the productions:
S-aSbS/ bSaS/€
Prove that L(G) is the set of all strings with an equal number of a’s and b’s.
Module-6
Q58. Reduce the following grammar G to CNF.
G is S-aAD
A→aB/bAB
B→b.
D→d.
Q59. Find whether the following language are context free or not.
(i) L={a p /p is prime}.
(ii) {a m b m c n /m ≤ n ≤ 2m}
Q60. Find whether the following languages are context free or not
{0 i 1 j / j=i 2 }
Q61. Convert the grammar S→AB, A- BS/b
B→SA/a in to GNF.