Final answer:
While converting an NFA to a DFA, the DFA often initially has more states than the NFA due to state explosion. This is the result of the subset construction algorithm, which accounts for all possible state combinations. However, after minimization, the DFA could have the same number or fewer states than the NFA.
Step-by-step explanation:
When converting an NFA to DFA, it is not necessary for the resulting DFA to have at least as many states as the original NFA. In fact, often the DFA will have more states due to the process of state explosion, which occurs because the DFA representation needs to account for all possible combinations of NFA states that could be reached by a string at any given time. However, there are cases where the NFA has redundant states or can be optimized such that the resultant DFA has the same number or fewer states.
The NFA to DFA conversion utilizes the subset construction algorithm. This algorithm involves creating a state in the DFA for each possible subset of NFA states. While the minimal DFA generated from an NFA will not have fewer states than the NFA in terms of recognizing the same language, the number of states before minimization can be substantially higher--potentially up to 2^n if n is the number of states in the NFA.
Lastly, after content loaded converting an NFA to DFA, DFA minimization algorithms can be applied to reduce the number of states, potentially bringing it down to the same size as or even smaller than the original NFA, if certain states are equivalent and can be merged.