Context free languages and Push-down automata

Question 81

CFG (Context Free Grammar) is not closed under

• Union
• Complementation
• Kleene star
• Product

Question 82

A CFG(Context Free Grammar) is said to be in Chomsky Normal 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 products to be used is

• 2x - 1
• 2x
• 2x + 1
• 2^x

Question 83

Pushdown automata can recognize language generated by_________.

• Only context free grammar
• Only regular grammar
• Context free grammar or rergular gramma
• Only context sensitive grammar

Question 84

To obtain a string of n Terminals from a given Chomsky normal form grammar, the number of productions to be used is:

• 2n - 1

• 2n

• n + 1

• n ²

Question 85

Consider the following two Grammars : G₁ : S → SbS|a G₂ : S → aB|ab, A→GAB|a, B→ABb|b Which of the following option is correct ?

• Only G₁ is ambiguous
• Only G₂ is ambiguous
• Both G₁ and G ₂are ambiguous
• Both G₁ and G₂are not ambiguous

Question 86

Context sensitive language can be recognized by a :

• Finite state machine
• Deterministic finite automata
• Non-deterministic finite automata
• Linear bounded automata

Question 87

The set A={ 0ⁿ 1ⁿ 2 ⁿ | n=1, 2, 3, ......... } is an example of a grammar that is:

• Context sensitive
• Context free
• Regular
• None of the above

Question 88

Consider the language L = { aⁿ ∣ n≥0 }∪{ aⁿbⁿ ∣ n≥0 } and the following statements.

• I. L is deterministic context-free.
• II. L is context-free but not deterministic context-free.
• III. L is not LL(k) for any k.

Which of the above statements is/are TRUE ?

• Ⅰ only

• Ⅱ only

• Ⅰ and Ⅲ only

• Ⅲ only

Question 89

In a pushdown automaton P=(Q,Σ,Γ,δ,q0,F), a transition of the form, where p,q∈Q, a∈σ∪{ϵ}, X,Y,∈Γ∪{ϵ}, represents

(q,Y) ∈ δ(p,a,X) 

Consider the following pushdown automaton over the input alphabet Σ={a,b} and stack alphabet Γ={#,A}. The number of strings of length 100 accepted by the above pushdown automaton is ___________ .

• 50
• 100
• 55
• 45

Question 90

Let L₁ be a regular language and L₂ be a context-free language. Which of the following languages is/are context-free?

• L₁∩L₂\'
• (L₁\'∪L₂\')\'
• L₁∪(L₂∪L₂\')
• (L₁∩L₂)∪(L₁∩L₂)