Question 1 |

Consider the language L over the alphabet {0, 1}, given below:

L = \{w \in \{0, 1\}^* | w \text{ does not contain three or more consecutive 1's} \}.

The minimum number of states in a Deterministic Finite-State Automaton (DFA) for L is _____.

L = \{w \in \{0, 1\}^* | w \text{ does not contain three or more consecutive 1's} \}.

The minimum number of states in a Deterministic Finite-State Automaton (DFA) for L is _____.

3 | |

4 | |

5 | |

6 |

Question 1 Explanation:

Question 2 |

Which one of the following regular expressions correctly represents the language of the finite automaton given below?

ab*bab* + ba*aba* | |

(ab*b)*ab* + (ba*a)*ba* | |

(ab*b + ba*a)*(a* + b*) | |

(ba*a + ab*b)*(ab* + ba*) |

Question 2 Explanation:

Question 3 |

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 3 Explanation:

Question 4 |

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 4 Explanation:

Question 5 |

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 5 Explanation:

There are 5 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.

In question 37, option C is also true.