Regular languages and finite automata

Question 121

The following Finite Automaton recognizes which of the given languages?

• {1, 0}* {01}
• {1, 0}* {1}
• {1}{1, 0}* {1}
• 1*0* {0, 1}

Question 122

The regular grammar for the language L = {aⁿb^m | n + m is even} is given by

• S → S₁ | S₂ S₁ → a S₁| A₁ A₁ → b A₁| λ S₂ → aaS₂| A₂ A₂ → b A₂| λ
• S → S₁ | S₂ S₁ → a S₁| aA₁ S₂ → aaS₂| A₂ A₁ → b A₁| λ A₂ → b A₂| λ
• S → S₁ | S₂ S₁ → aaa S₁| aA₁ S₂ → aaS₂| A₂ A₁ → b A₁| λ A₂ → b A₂| λ
• S → S₁ | S₂ S₁ → aa S₁| A₁ S₂ → aaS₂| A₂ A₁ → bb A₁| λ A₂ → bb A₂| λ

Question 123

Let Σ = {a, b} and language L = {aa, bb}. Then, the complement of L is

• {λ, a, b, ab, ba} ∪ {w∈{a, b}* | |w| > 3}

• {a, b, ab, ba} ∪ {w∈{a, b}* | |w| > 3}

• {w ∈ { a, b}* | |w| > 3} ∪ {a, b, ab, ba}

• {λ, a, b, ab, ba} ∪ {w ∈ {a, b}* | |w| ≥ 3}

Question 124

Consider the following identities for regular expressions: (a) (r + s)* = (s + r)* (b) (r*)* = r* (c) (r* s*)* = (r + s)* Which of the above identities are true?

• (a) and (b) only
• (b) and (c) only
• (c) and (a) only
• (a), (b) and (c)

Question 125

Given the following two languages : L1 = {uww^Rν | u, v, w ∈ {a, b}⁺} L2 = {uww^Rν | u, ν, w ∈ {a, b}⁺, |u| > |ν|} Which of the following is correct ?

• L₁ is regular language and L₂ is not regular language.
• L₁ is not regular language and L₂ is regular language.
• Both L₁ and L₂ are regular languages.
• Both L₁ and L₂are not regular languages.

Question 126

The number of strings of length 4 that are generated by the regular expression (0|∈)1⁺2* (3|∈), where | is an alternation character, {+, *} are quantification characters, and ∈ is the null string, is :

• 08
• 10
• 11
• 12

Question 127

The regular expression for the complement of the language L = {aⁿb_m|n ≥ 4, m ≤ 3} is:

• (λ + a + aa + aaa) b* + a* bbbb* + (a + b)* ba(a + b)*
• (λ + a + aa + aaa) b* + a* bbbbb* + (a + b)* ab(a + b)*
• (λ + a + aa + aaa) + a* bbbbb* + (a + b)* ab(a + b)*
• (λ + a + aa + aaa)b* + a* bbbbb* + (a + b)* ba(a + b)*

Question 128

Let L be the language generated by regular expression 0*10* and accepted by the deterministic finite automata M. Consider the relation R_M defined by M. As all states are reachable from the start state, R_M has _____ equivalence classes.

• 2
• 4
• 5
• 6

Question 129

What are the final states of the DFA generated from the following NFA?

• q₀, q₁, q₂
• [q₀, q₁], [q₀, q₂], [ ]
• q₀, [q₁, q₂]
• [q₀, q₁], q₂

Question 130

There are exactly __________ different finite automata with three states x, y and z over the alphabet {a, b} where x is always the start state.

• 64
• 56
• 1024
• 5832