Practice Test: Question Set - 10
1. Which of the following definitions below generates the same language as L, where
L = {xn yn such that n > = 1} ?
I. E —> xEy | xy- (A) I only
- (B) I and II
- (C) II and III
- (D) II only
2. Following context free grammar
S —> aB | bA
A —>b | aS | bAA
B —> b | bS | aBB
generates strings of terminals that have
- (A) Equal number
of a's and b's
- (B) Odd number
of a's and odd number b's
- (C) Even number
of a's and even number of b's
- (D) Odd number
of a's and even number of a's
3. Set of regular languages over a given alphabet set is closed under
- (A) Union
- (B) Complementation
- (C) Intersection
- (D) All of these
4. Consider the grammar:
S —> ABCc | Abc
BA —> AB
Bb —> bb
Ab —> ab
Aa —> aa
Which of the following sentences can be
derived by this grammar?
- (A) abc
- (B) aab
- (C) abcc
- (D) abbb
5. Define for a context free language
L ≤ {0 ; 1} init (L) = {u/uv ε L for some v in {0,1}}
(in other words, init (L) is the set of prefixes of L)
Let L {w/w is noempty and has an equal number of 0’s and 1’s)
Then init (L) is
- (A) Set of all
binary strings with unequal number of 0’s and 1’s
- (B) Set of all
binary strings including the null string
- (C) Set of all
binary strings with exactly one more 0’s than the number of 1’s or 1 more
than the number of 0’s
- (D) None of
these
6. Which of the following conversion is not possible (algorithmically)?
- (A) Regular
grammar to context-free grammar
- (B) Nondeterministic
FSA to deterministic FSA
- (C) Nondeterministic
PDA to deterministic PDA
- (D) Nondeterministic
TM to deterministic TM
7. For two regular languages
L1 = (a + b)* a and L2 =
b (a + b) *
The intersection of L1 and L2 is given by
- (A) (a + b ) *
ab
- (B) ab (a + b )
*
- (C) a ( a + b )
* b
- (D) b (a + b ) *
a
8. For which of the following application, regular expressions cannot be used?
- (A) Designing
computers
- (B) Designing
compilers
- (C) Both (a) and
(b)
- (D) Developing
computers
9. If G = ({S}, {a}, {S -> SS), S),
then language generated by G is
- (A) L (G) = φ
- (B) L(G) = an
- (C) L (G) = a*
- (D) L (G) = anban
10. Recursively enumerable languages are not closed under
- (A) Union
- (B) Homomorphism
- (C) Complementation
- (D) Concatenation
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