Regular languages and finite automata

Question 41

Consider the following languages [tex]L1=\\left \\{ ww|w\\in \\left \\{ a,b \\right \\}*\\right \\}[/tex] [tex]L2=\\left \\{ ww^{R}|w\\in \\left \\{ a,b \\right \\}*, w^{R} is\\ the\\ reverse\\ of\\right\\ w \\}[/tex] [tex]L3=\\left \\{ 0^{2i}| i\\ is\\ an\\ integer \\}[/tex] [tex]L4=\\left \\{ 0^{i^{2}}| i\\ is\\ an\\ integer \\}[/tex] Which of the languages are regular?

• Only L1 and L2

• Only L2, L3 and L4

• Only L3 and L4

• Only L3

Question 42

Let S and T be language over Σ = {a,b} represented by the regular expressions (a+b*)* and (a+b)*, respectively. Which of the following is true?

• S ⊂ T
• T ⊂ S
• S = T
• S ∩ T = φ

Question 43

Let L denotes the language generated by the grammar S -> 0S0/00. Which of the following is true?

• L = 0+

• L is regular but not 0+

• L is context free but not regular

• L is not context free

Question 44

What can be said about a regular language L over {a} whose minimal finite state automaton has two states?

• L must be {aⁿ| n is odd}
• L must be {aⁿ| n is even}
• L must be {aⁿ| ³ O}
• Either L must be {aⁿ | n is odd}, or L must be {aⁿ | n is even}

Question 45

Consider the following Deterministic Finite Automata Which of the following is true?

• It only accepts strings with prefix as "aababb"
• It only accepts strings with substring as "aababb"
• It only accepts strings with suffix as "aababb"
• None of the above

Question 46

How many minimum states are required in a DFA to find whether a given binary string has odd number of 0\'s or not, there can be any number of 1\'s.

• 1
• 2
• 3
• 4

Question 47

Consider the DFAs M and N given above. The number of states in a minimal DFA that accepts the language L(M) ∩ L(N) is __________.

• 0

• 1

• 2

• 3

Question 48

Consider alphabet ∑ = {0, 1}, the null/empty string λ and the sets of strings X₀, X₁ and X₂ generated by the corresponding non-terminals of a regular grammar. X₀, X₁ and X₂ are related as follows:

X0 = 1 X1
X1 = 0 X1 + 1 X2
X2 = 0 X1 + {λ} 

Which one of the following choices precisely represents the strings in X₀?

• 10 (0* + (10)*)1
• 10 (0* + (10)*)*1
• 1(0* + 10)*1
• 10 (0 + 10)*1 + 110 (0 + 10)*1

Question 49

Which of the following languages is/are regular?

L1: {wxwR ⎪ w, x ∈ {a, b}* and ⎪w⎪, ⎪x⎪ >0} wR is the reverse of string w
L2: {anbm ⎪m ≠ n and m, n≥0
L3: {apbqcr ⎪ p, q, r ≥ 0}  

• L1 and L3 only
• L2 only
• L2 and L3 only
• L3 only

Question 50

The number of states in the minimal deterministic finite automaton corresponding to the regular expression (0 + 1)*(10) is ____________

• 2
• 3
• 4
• 5