Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Design a NFA for the language:L: {an| n is ev...
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Design a NFA for the language:
L: {an| n is even or divisible by 3}
Which of the following methods can be used to simulate the same.
L: {an| n is even or divisible by 3}
Which of the following methods can be used to simulate the same.
- a)e-NFA
- b)Power Construction Method
- c)Both (a) and (b)
- d)None of the mentioned
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Design a NFA for the language:L: {an| n is even or divisible by 3}Whic...
It is more convenient to simulate a machine using e-NFA else the method of Power Construction is used from the union-closure of DFA’s.
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Design a NFA for the language:L: {an| n is even or divisible by 3}Whic...
NFA for the language L: {an| n is even or divisible by 3}
To design an NFA for the language L, we need to consider two conditions:
1. n is even
2. n is divisible by 3
We can design an NFA for each of these conditions individually and then combine them to form an NFA for the language L.
NFA for n is even:
1. Start state with epsilon transition to state A
2. From state A, on input 'a', transition to state B
3. From state B, on input 'a', transition to state A
4. Final state: state A
NFA for n is divisible by 3:
1. Start state with epsilon transition to state C
2. From state C, on input 'a', transition to state D
3. From state D, on input 'a', transition to state E
4. From state E, on input 'a', transition to state C
5. Final state: state C
Combining both NFAs:
1. Combine the start states of both NFAs into a single start state
2. Combine all final states of both NFAs into a single final state
3. Combine all transitions from both NFAs
This NFA accepts all strings where the length of the string is even or divisible by 3.
Which of the following methods can be used to simulate the same?
Neither e-NFA nor Power Construction Method can be used to simulate the same. Both of them are used to convert an NFA to a DFA. Since we already have an NFA for the language L, we cannot use either of these methods. Hence, the correct answer is "None of the mentioned".
To design an NFA for the language L, we need to consider two conditions:
1. n is even
2. n is divisible by 3
We can design an NFA for each of these conditions individually and then combine them to form an NFA for the language L.
NFA for n is even:
1. Start state with epsilon transition to state A
2. From state A, on input 'a', transition to state B
3. From state B, on input 'a', transition to state A
4. Final state: state A
NFA for n is divisible by 3:
1. Start state with epsilon transition to state C
2. From state C, on input 'a', transition to state D
3. From state D, on input 'a', transition to state E
4. From state E, on input 'a', transition to state C
5. Final state: state C
Combining both NFAs:
1. Combine the start states of both NFAs into a single start state
2. Combine all final states of both NFAs into a single final state
3. Combine all transitions from both NFAs
This NFA accepts all strings where the length of the string is even or divisible by 3.
Which of the following methods can be used to simulate the same?
Neither e-NFA nor Power Construction Method can be used to simulate the same. Both of them are used to convert an NFA to a DFA. Since we already have an NFA for the language L, we cannot use either of these methods. Hence, the correct answer is "None of the mentioned".
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