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6 6 votes

Consider a Finite State Automaton (FSA) $\mathbf{M1}$ designed to recognize a specific language over the alphabet $\{0,1\}$.
 


Which of the following best describes the language $\mathbf{L}(\mathbf{M1})$ accepted by this automaton?
 

  1. All strings that contain at least four $1$'s.
     
  2. All strings that end with the substring "$01110$".
     
  3. All strings that contain the substring "$01110$".
     
  4. All strings that have exactly three $1$'s followed by a $0$.

6 Answers

1 1 vote
It would be B,C in msq and c in mcq because the machine aggrees to take 01110 and even if we repaeat after 0 it goes on loop which tells that it even if string has 0 and 1s after the main substring machine is supposed to find out it will eventually accept and if even it ends on 0 it will be accepted. And C in mcq because C is a bigger set whose subset is B i.e. containing the substring is a super set of the set of strings that end with the required substring. Thank You.
1 1 vote
C

for B as final state have self (0,1). it can end with (0+1)*   so option B  X

contains Atlest 3 '1,s'  so option A  X

 
1 1 vote
$A. False, 1111\ has\ at\ least\ 4\ ones\ but\ is\ not\ accepted$

$B.False, 011101 \in L_m\ but\ it\ does\ not\ end\ with\ given\ string\ 0111.$

$D.as\ no\  0's\ in \ 1,11,111\ still \ not\ accepted.$

Hence Answer is C
0 0 votes

For option a counter example is 01110 is accepted but a/q to option a it should not be accepted

For option b after 01110 it should not come anything but in given dfa it (0+1)^* is coming

For option d it is saying it three one is coming it should be followed by 0 , but if three one is not coming it should be accepted like 1, 11 but they are not accepted.

So option C is correct 

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