Regular languages and finite automata

Question 31

The following diagram represents a finite state machine which takes as input a binary number from the least significant bit. Which one of the following is TRUE?

• It computes 1\'s complement of the input number
• It computes 2\'s complement of the input number
• It increments the input number
• It decrements the input number

Question 32

The following finite state machine accepts all those binary strings in which the number of 1\'s and 0\'s are respectively.

• divisible by 3 and 2
• odd and even
• even and odd
• divisible by 2 and 3

Question 33

The regular expression 0*(10*)* denotes the same set as

• (1*0)*1*
• 0 + (0 + 10)*
• (0 + 1)* 10(0 + 1)*
• none of these

Question 34

Consider the following deterministic finite state automaton M. Let S denote the set of seven bit binary strings in which the first, the fourth, and the last bits are 1. The number of strings in S that are accepted by M is

• 1
• 5
• 7
• 8

Question 35

Consider the NFA M shown below.                           

[caption width="800"] [/caption]

 Let the language accepted by M be L. Let L1 be the language accepted by the NFA M1, obtained by changing the accepting state of M to a non-accepting state and by changing the non-accepting state of M to accepting states. Which of the following statements is true ?

• L1 = {0, 1}* - L

• L1 = {0, 1}*

• L1 ⊆ L

• L1 = L

Question 36

The Finite state machine described by the following state diagram with A as starting state, where an arc label is x / y and x stands for 1-bit input and y stands for 2- bit output

• Outputs the sum of the present and the previous bits of the input.
• Outputs 01 whenever the input sequence contains 11.
• Outputs 00 whenever the input sequence contains 10.
• None of these

Question 37

The smallest finite automation which accepts the language {x | length of x is divisible by 3} has :

• 2 states
• 3 states
• 4 states
• 5 states

Question 38

Consider the following two statements:

• Only S1 is correct
• Only S2 is correct
• Both S1 and S2 are correct
• None of S1 and S2 is correct

Question 39

Given an arbitary non-deterministic finite automaton (NFA) with N states, the maximum number of states in an equivalent minimized DFA is at least

• N²
• 2^N
• 2N
• N!

Question 40

Consider a DFA over ∑ = {a, b} accepting all strings which have number of a’s divisible by 6 and number of b’s divisible by 8. What is the minimum number of states that the DFA will have?

• 8
• 14
• 15
• 48