Regular languages and finite automata

Question 11

Which of the following statements is false?

• Every NFA can be converted to an equivalent DFA
• Every non-deterministic Turing machine can be converted to an equivalent deterministic Turing machine
• Every regular language is also a context-free language
• Every subset of a recursively enumerable set is recursive

Question 12

Given below are two finite state automata (→ indicates the start state and F indicates a final state)Which of the following represents the product automaton Z×Y? 

[caption width="800"] [/caption]

• A

• B

• C

• D

Question 13

Match the following NFAs with the regular expressions they correspond to

 1. ϵ + 0(01*1 + 00) * 01*
 2. ϵ + 0(10 *1 + 00) * 0
 3. ϵ + 0(10 *1 + 10) *1
 4. ϵ + 0(10 *1 + 10) *10 *

[caption width="800"] [/caption]

• P - 2, Q - 1, R - 3, S - 4

• P - 1, Q - 3, R - 2, S - 4

• P - 1, Q - 2, R - 3, S - 4

• P - 3, Q - 2, R - 1, S - 4

Question 14

Which of the following are regular sets?

• {aⁿb^2m|n≥0, m≥0}

• {aⁿb^m | n = 2m}

•  {aⁿb^m n≠m}

•  {xcy | x,y ∈ {a,b}*}

Question 15

Consider the following Deterministic Finite Automaton. Let denote the set of eight bit strings whose second, third, sixth and seventh bits are 1. The number of strings in that are accepted by M is

• 0
• 1
• 2
• 3

Question 16

Which of the following is TRUE?

• Every subset of a regular set is regular.
• Every finite subset of a non-regular set is regular.
• The union of two non-regular sets is not regular.
• Infinite union of finite sets is regular.

Question 17

A minimum state deterministic finite automaton accepting the language L={w | w ε {0,1} *, number of 0s and 1s in w are divisible by 3 and 5, respectively} has

• 15 states

• 11 states

• 10 states

• 9 states

Question 18

Which of the following languages is regular? 

• {ww^R|w ∈ {0,1}⁺} 

• {ww^Rx|x,w∈{0,1}⁺}

• {wxw^R|x,w∈{0,1}⁺}

• {xww^R|x,w∈{0,1}⁺}

Question 19

Consider the following Finite State Automaton. The language accepted by this automaton is given by the regular expression

• A
• B
• C
• D

Question 20

Consider the automata given in previous question. The minimum state automaton equivalent to the above FSA has the following number of states

• 1

• 2

• 3

• 4