Finite Automata PYQ QUIZ GATE CS

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Question 1

Consider the set of strings on {0,1} in which, every substring of 3 symbols has at most two zeros. For example, 001110 and 011001 are in the language, but 100010 is not. All strings of length less than 3 are also in the language. A partially completed DFA that accepts this language is shown below. 

 

 The missing arcs in the DFA are 

  •  
  •  
  •  
  •  

Question 2

Consider the DFA given. 

 

 Which of the following are FALSE?

  • Complement of L(A) is context-free.

  • L(A) = L((11*0+0)(0 + 1)*0*1*).

  • For the language accepted by A, A is the minimal DFA.

  • A accepts all strings over {0, 1} of length at least 2.

Question 3

Which of the following pairs have DIFFERENT expressive power?

  • Deterministic finite automata(DFA) and Non-deterministic finite automata(NFA)

  • Deterministic push down automata(DPDA)and Non-deterministic push down automata(NPDA)

  • Deterministic single-tape Turing machine and Non-deterministic single-tape Turing machine

  • Single-tape Turing machine and multi-tape Turing machine

Question 4

Definition of a language L with alphabet {a} is given as following.

             L={|ank|k>0, and n is a positive integer constant}

What is the minimum number of states needed in DFA to recognize L?

  • k+1

  • n+1

  • 2(n+1)

  • 2[Tex](k+1)[/Tex]

Question 5

A deterministic finite automation (DFA)D with alphabet {a,b} is given below

GATE2011AT1

Which of the following finite state machines is a valid minimal DFA which accepts the same language as D?

GATE2011AT2
GATE2011AT3

  • A

  • B

  • C

  • D

Question 6

Let w be any string of length n is {0,1}*. Let L be the set of all substrings of w. What is the minimum number of states in a non-deterministic finite automaton that accepts L?

  • n-1

  • n

  • n+1

  • 2n-1

Question 7

Let L={w in (0 + 1)*|w has even number of 1s}, i.e. L is the set of all bit strings with even number of 1s. Which one of the regular expression below represents L?

  • (0*10*1)*

  • 0*(10*10*)*

  • 0*(10*1*)*0*

  • 0*1(10*1)*10*

Question 8

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 9

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
GATECS2002Q28

  • 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 10

Which of the regular expressions given below represent the following DFA?

GATECS2014Q45

I) 0*1(1+00*1)*
II) 0*1*1+11*0*1
III) (0+1)*1

  • I and II only

  • I and III only

  • II and III only

  • I, II, and III

There are 51 questions to complete.

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