Question 1 |

Suppose we want to design a synchronous circuit that processes a string of 0's and 1's. Given a string, it produces another string by replacing the first 1 in any subsequence of consecutive 1's by a 0. Consider the following example.

\begin{array}{ll} \text{Input sequence:} & 00100011000011100 \\ \text{Output sequence:} & 00000001000001100 \end{array}

A Mealy Machine is a state machine where both the next state and the output are functions of the present state and the current input.

The above mentioned circuit can be designed as a two-state Mealy machine. The states in the Mealy machine can be represented using Boolean values 0 and 1. We denote the current state, the next state, the next incoming bit, and the output bit of the Mealy machine by the variables s, t, b and y respectively.

Assume the initial state of the Mealy machine is 0.

What are the Boolean expressions corresponding to t and y in terms of s and b?

\begin{array}{ll} \text{Input sequence:} & 00100011000011100 \\ \text{Output sequence:} & 00000001000001100 \end{array}

A Mealy Machine is a state machine where both the next state and the output are functions of the present state and the current input.

The above mentioned circuit can be designed as a two-state Mealy machine. The states in the Mealy machine can be represented using Boolean values 0 and 1. We denote the current state, the next state, the next incoming bit, and the output bit of the Mealy machine by the variables s, t, b and y respectively.

Assume the initial state of the Mealy machine is 0.

What are the Boolean expressions corresponding to t and y in terms of s and b?

t=s+b y=sb | |

t=b y=sb | |

t=b y=s\bar{b} | |

t=s+b y=s\bar{b} |

Question 1 Explanation:

Question 2 |

Consider the following deterministic finite automaton (DFA)

The number of strings of length 8 accepted by the above automaton is _________

The number of strings of length 8 accepted by the above automaton is _________

32 | |

256 | |

64 | |

512 |

Question 2 Explanation:

Question 3 |

Consider the following language:

L= \{ w \in \{0,1\}^* \mid w \text{ ends with the substring } 011 \}

Which one of the following deterministic finite automata accepts L?

L= \{ w \in \{0,1\}^* \mid w \text{ ends with the substring } 011 \}

Which one of the following deterministic finite automata accepts L?

A | |

B | |

C | |

D |

Question 3 Explanation:

Question 4 |

Minimum number of states required in DFA accepting binary strings not ending in "101" is

3 | |

4 | |

5 | |

6 |

Question 4 Explanation:

Question 5 |

Consider the following language.

L={x \in \{a,b\}^*| number of a's in x divisible by 2 but not divisible by 3}

The minimum number of states in DFA that accepts L is _______

L={x \in \{a,b\}^*| number of a's in x divisible by 2 but not divisible by 3}

The minimum number of states in DFA that accepts L is _______

4 | |

5 | |

6 | |

7 |

Question 5 Explanation:

Question 6 |

Let \Sigma be the set of all bijections from {1,...,5} to {1,...,5}, where id denotes the identity function, i.e. id(j)=j,\forall j. Let \circ denote composition on functions. For a string x = x_1x_2 ... x_n \in \Sigma ^n, n \geq 0, let \pi(x) = x_1\circ x_2\circ ... \circ x_n. Consider the language L = \{x \in \Sigma ^* | \pi(x) = id\}. The minimum number of states in any DFA accepting L is _________ .

25 | |

125 | |

120 | |

150 |

Question 6 Explanation:

Question 7 |

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

Complements a given bit pattern | |

Finds 2^{\prime} s complement of a given bit pattern | |

Increments a given bit pattern by 1 | |

Changes the sign bit |

Question 7 Explanation:

Question 8 |

Given a language L, define L^{i} as follows:

L^{0}=\{\varepsilon \}

L^{i}=L^{i-1} \cdot L for all i \gt 0

The order of a language L is defined as the smallest k such that L^{k}=L^{k+1}. Consider the language L1 (over alphabet 0) accepted by the following automaton.

The order of L1 is ______

L^{0}=\{\varepsilon \}

L^{i}=L^{i-1} \cdot L for all i \gt 0

The order of a language L is defined as the smallest k such that L^{k}=L^{k+1}. Consider the language L1 (over alphabet 0) accepted by the following automaton.

The order of L1 is ______

1 | |

2 | |

3 | |

4 |

Question 8 Explanation:

Question 9 |

Let N be an NFA with n states. Let k be the number of states of a minimal DFA which is equivalent to N. Which one of the following is necessarily true?

k\geqslant 2^{n} | |

k\geqslant n | |

k\leqslant n^{2} | |

k\leqslant 2^{n} |

Question 9 Explanation:

Question 10 |

Let \delta denote that transition function and \hat{\delta} denote the extended transition function of the \epsilon- NFA whose transition table is given below:

Then \hat{\delta}(q_{2},aba) is ____

Then \hat{\delta}(q_{2},aba) is ____

\varnothing | |

\{q_{0},q_{1},q_{3}\} | |

\{q_{0},q_{1},q_{2}\} | |

\{q_{0},q_{2},q_{3}\} |

Question 10 Explanation:

There are 10 questions to complete.

question no 7’s Diagram is wrong

Thank you Shivam,

We have updated the figure.

question no 49th question is wrong .second term will be only of 5 1’s not of 6 1s.

Thank you shivam,

We have updated the question.

In Que.64 Option (A) is also False. (Correct answer in GateOverflow- False. Conversion from NPDA To DPDA is not always possible like in the case of wwR.)

Thank You Rashmi,

We have updated the option.

In question, 66 state table is not containing all elements.

Thank You Rashmi,

We have updated the figure in question.

In question, 64 Option (A) is also False. (Correct answer in GateOverflow- False. Conversion from NPDA To DPDA is not always possible like in the case of wwR.)

In question, 67 option (A) is (01) instead of (1).

Thank You Rashmi,

We have updated the option.