Regular languages and finite automata

Question 21

Which one of the following is TRUE? 

• The language L = {aⁿbⁿ | n ≥ 0} is regular.

•  The language L = {aⁿ| n is prime} is regular.

• The language L = {w|w has 3k + 1 b's for some k ∈N with Σ = {a, b}} is regular. 

• The language L = {ww | we Σ* with Σ = {0,1}} is regular.

Question 22

• {q0, q1, q2}
• {q0, q1}
• {q0, q1, q2, q3}
• {q3}

Question 23

Which of the regular expressions given below represent the following DFA?

I) 0*1(1+00*1)*
II) 0*1*1+11*0*1
III) (0+1)*1 

• I and II only
• I and III only
• II and III only
• I, II, and III

Question 24

Which one of the following is CORRECT?

• Only (I)
• Only (II)
• Both (I) and (II)
• Neither (I) nor (II)

Question 25

Let L1 = {w ∈ {0,1}^∗ | w has at least as many occurrences of (110)’s as (011)’s}. 
Let L2 = { ∈ {0,1}^∗ | w has at least as many occurrences of (000)’s as (111)’s}. 

Which one of the following is TRUE?

• L1 is regular but not L2

• L2 is regular but not L!

• Both L2 and L1 are regular

• Neither L1 nor L2 are regular

Question 26

The length of the shortest string NOT in the language (over Σ = {a, b}) of the following regular expression is ______________.

a*b*(ba)*a*

• 2
• 3
• 4
• 5

Question 27

If s is a string over (0 + 1)* then let n₀(s) denote the number of 0’s in s and n₁(s) the number of 1’s in s. Which one of the following languages is not regular? 7" />

• A
• B
• C
• D

Question 28

Consider the regular language L = (111 + 11111)*. The minimum number of states in any DFA accepting this languages is:

• 3

• 5

• 8

• 9

Question 29

Consider the machine M: 

The language recognized by M is :

• {w ∈ {a, b}* / every a in w is followed by ex­actly two b\'s}
  

• {w ∈ {a, b}* every a in w is followed by at least two b’}
  

• {w ∈ {a, b}* w contains the substring \'abb\'}
  

• {w ∈ {a, b}* w does not contain \'aa\' as a substring}
  

Question 30

Let Nf and Np denote the classes of languages accepted by non-deterministic finite automata and non-deterministic push-down automata, respectively. Let Df and Dp denote the classes of languages accepted by deterministic finite automata and deterministic push-down automata, respectively. Which one of the following is TRUE?

• Df ⊂ Nf and Dp ⊂ Np
• Df ⊂ Nf and Dp = Np
• Df = Nf and Dp = Np
• Df = Nf and Dp ⊂ Np