Intermediate
Theory of Computation
Q79 / 100
How does the subset construction explain why an n-state NFA can require up to 2ⁿ states when converted to a DFA?
Correct! Well done.
Incorrect.
The correct answer is B) Because each DFA state represents a distinct subset of the NFA's state set, and there are 2ⁿ possible subsets of an n-element set, all of which may be reachable for some languages
B
Correct Answer
Because each DFA state represents a distinct subset of the NFA's state set, and there are 2ⁿ possible subsets of an n-element set, all of which may be reachable for some languages
Explanation
In the subset (powerset) construction, each DFA state is the set of NFA states reachable on a given input prefix. Since an n-element set has 2ⁿ subsets, certain NFAs (carefully designed) force all of them to be distinguishable, giving a tight exponential blow-up.
Progress
79/100