Classical

Theory Of Computation MCQ - Context free languages

1:  

Correct hierarchical relationship among context- free, right-linear, and context-sensitive language is

A.

context-free  ⊂ right-linear  ⊂ context-sensitive

B.

context-free  ⊂ context-sensitive  ⊂ right-linear

C.

context-sensitive  ⊂ right-inear  ⊂context-free

D.

right-linear  ⊂context-free  ⊂context-sensitive

 
 

Option: D

Explanation :


2:  

In the following grammar :

x : : = x  ⊕ y |  4
y : : = z * y I 2
z : : = id


which of the folowing is true ?

A.

⊕ is left associative while * is right associative

B.

Both ⊕ and * are left associative

C.

⊕ is right associative while * is left associative

D.

None of these

 
 

Option: B

Explanation :


3:  

Which of the following CFG's can't be simulated by an FSM ?

A.

S --> Sa | b

B.

S  --> aSb | ab

C.

S --> abX,  X --> cY,  Y --> d | aX

 

D.

None of these

 
 

Option: B

Explanation :

Option (b) generates the set {an bn ,n=1,2,3 ....}which is not regular ,Option (a) is left linear where as option (C) is right linear .


4:  

ADG is said to be in Chomsky Form (CNF), if all the productions are of the form A --> BC or
A --> a. Let G be a CFG in CNF. To derive a string of terminals of length x , the number of productions to be used is

A. 2x - 1
B. 2x
C. 2x + I
D. None of these
 
 

Option: A

Explanation :


5:  

Which of the following statements is correct?

A.

A = { If an bn  | n = 0,1, 2, 3 ..} is regular language

B.

Set B of all strings of equal number of a's and b's deines a regular language

C.

L (A* B*)∩ B gives the set A

D.

None of these

 
 

Option: C

Explanation :

If we include A and B in a set and if we write A*  it means except  then A i.e. B  same as  B*  means except then B i.e.A so  if we intersect (A*B*)  and B   then get A  because in any regular language

 if we write A-B then A-B=A intersection B'  so if we intersect A and B means A-B  So intersection of (A*B*) and B  = (BA) intersection B  means (BA)-B' and B'=A so (BA) intersection(A)=A
So ans is (C) 




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Syllabus covered in this section is-

  • Regular languages and finite automata
  • Context free languages and Push-down automata
  • Recursively enumerable sets and Turing machines
  • Undecidability, NPcompleteness
  • Models of computation-Finite Automata
  • Pushdown Automata
  • Non-detenninism and NFA. DPDA and PDAs and Languages accepted by these Structures
  • Grammars, Languages,
  • Non- computability and Examples of non-computable problems

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