Regular languages and finite automata

Question 131

Consider a language A defined over the alphabet = {0, 1} as The expression The expression means the floor of n/2, or what you get by rounding n/2 down to the nearest integer. Which of the following is not an example of a string in A?

• 011
• 0111
• 0011
• 001111

Question 132

Minimal deterministic finite automaton for the language L = {0ⁿ | n ≥ 0, n ≠ 4} will have:

• 1 final state among 5 states
• 4 final states among 5 states
• 1 final state among 6 states
• 5 final states among 6 states

Question 133

The regular expression corresponding to the language L where L = { x ϵ {0, 1}*|x ends with 1 and does not contain substring 00 } is:

• (1 + 01) * (10 + 01)
• (1 + 01) * 01
• (1 + 01) * (1 + 01)
• (10 + 01) * 01

Question 134

The transition function for the language L = {w|n_a (w) and n_b(w) are both odd} is given by: δ (q₀, a) = q₁ ; δ (q₀, b) = q₂ δ (q₁, a) = q₀ ; δ (q₁, b) = q₃ δ (q₂, a) = q₃ ; δ (q₂, b) = q₀ δ (q₃, a) = q₂ ; δ (q₃, b) = q₁ The initial and final states of the automata are:

• q₀ and q₀respectively
• q₀ and q₁respectively
• q₀ and q₂respectively
• q₀ and q₃respectively

Question 135

Given two languages: L₁ = {(ab) ⁿ a^k | n > k, k ≥ 0} L₂ = {aⁿ b^m| n ≠ m} Using pumping lemma for regular language, it can be shown that

• L₁ is regular and L₂ is not regular.
• L₁ is not regular and L₂ is regular.
• L₁ is regular and L₂ is regular.
• L₁ is not regular and L₂ is not regular.

Question 136

Regular expression for the complement of language L = {aⁿ b^m | n ≥ 4, m ≤ 3} is

• (a + b)* ba(a + b)*
• a* bbbbb*
• (λ + a + aa + aaa)b* + (a + b)* ba(a + b)*
• None of the above

Question 137

The FSM (Finite State Machine) machine pictured in the figure above

• Complements a given bit pattern
• Finds 2\'s complement of a given bit pattern
• Increments a given bit pattern by 1
• Changes the sign bit

Question 138

Two finite state machines are said to be equivalent if they:

• Have the same number of edges
• Have the same number of states
• Recognize the same set of tokens
• Have the same number of states and edges

Question 139

The finite state machine given in figure below recognizes:

• any string of odd number of a’s
• any string of odd number of b’s
• any string of even number of a’s and odd number of b’s
• any string of odd number of a’s and odd number of b’s

Question 140

A pushdown automata behaves like a Turing machine when the number of auxiliary memory is:

• 0
• 1
• 1 or more
• 2 or more