Regular languages and finite automata

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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 

  •  
  •  
  •  
  •  
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Question 2

Consider the languages L1 = [Tex]\\phi [/Tex]and L2 = {a}. Which one of the following represents L1 L2* U L1*

 

  • {[Tex]\epsilon [/Tex]}

  • [Tex]\phi [/Tex]

  • a*

  • {[Tex]\epsilon [/Tex],a}

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Question 3

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.

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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]

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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

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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

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Question 7

Which one of the following languages over the alphabet {0,1} is described by the regular expression: (0+1)*0(0+1)*0(0+1)* ?

  • The set of all strings containing the substring 00.

  • The set of all strings containing at most two 0’s.

  • The set of all strings containing at least two 0’s.

  • The set of all strings that begin and end with either 0 or 1.

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Question 8

Which one of the following is FALSE?

  • There is unique minimal DFA for every regular language

  • Every NFA can be converted to an equivalent PDA.

  • Complement of every context-free language is recursive.

  • Every nondeterministic PDA can be converted to an equivalent deterministic PDA.

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Question 9

Given the following state table of an FSM with two states A and B, one input and one output:

Present State A      Present State B        Input         Next State A         Next State B      Output         
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1

If the initial state is A=0, B=0, what is the minimum length of an input string which will take the machine to the state A=0, B=1 with Output = 1?

  • 3

  • 4

  • 5

  • 6

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Question 10

Given the language L = {ab, aa, baa}, which of the following strings are in L*?

  • abaabaaabaa

  • aaaabaaaa

  • baaaaabaaaab

  •  baaaaabaa

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