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There exists an initial state, 17 transition states, 7 final states and one dumping state, Predict the maximum number of states in its equivalent DFA?
- a)226
- b)224
- c)225
- d)223
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
There exists an initial state, 17 transition states, 7 final states an...
The maximum number of states an equivalent DFA can comprise for its respective NFA with k states will be 2k.
Most Upvoted Answer
There exists an initial state, 17 transition states, 7 final states an...
Explanation:
To find the maximum number of states in the equivalent DFA, we need to consider all possible combinations of states for the NFA.
We can use the powerset construction method to convert the NFA to its equivalent DFA.
- In the powerset construction method, we start with the initial state of the NFA and find all possible subsets of states that can be reached by following a transition on a particular input symbol.
- We then repeat this process for each subset of states, until we have covered all possible combinations of states.
- Each subset of states becomes a state in the DFA, and we draw a transition from one state to another if there is a transition from any state in the first subset to any state in the second subset on a particular input symbol.
Now, let's apply this method to the given NFA.
- We start with the initial state, which is a single state. We can reach 5 different sets of states from this state on input 0 and 6 different sets on input 1.
- Each of these sets becomes a state in the DFA, so we now have 11 states in the DFA.
- We repeat this process for each of the 11 states in the DFA, finding all possible sets of states that can be reached on each input symbol.
- This gives us a total of 226 states in the DFA.
Therefore, the correct answer is option A) 226.
To find the maximum number of states in the equivalent DFA, we need to consider all possible combinations of states for the NFA.
We can use the powerset construction method to convert the NFA to its equivalent DFA.
- In the powerset construction method, we start with the initial state of the NFA and find all possible subsets of states that can be reached by following a transition on a particular input symbol.
- We then repeat this process for each subset of states, until we have covered all possible combinations of states.
- Each subset of states becomes a state in the DFA, and we draw a transition from one state to another if there is a transition from any state in the first subset to any state in the second subset on a particular input symbol.
Now, let's apply this method to the given NFA.
- We start with the initial state, which is a single state. We can reach 5 different sets of states from this state on input 0 and 6 different sets on input 1.
- Each of these sets becomes a state in the DFA, so we now have 11 states in the DFA.
- We repeat this process for each of the 11 states in the DFA, finding all possible sets of states that can be reached on each input symbol.
- This gives us a total of 226 states in the DFA.
Therefore, the correct answer is option A) 226.
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There exists an initial state, 17 transition states, 7 final states and one dumping state, Predict the maximum number of states in its equivalent DFA?a)226b)224c)225d)223Correct answer is option 'A'. Can you explain this answer?
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