Solution:

The given question is related to the conversion of NFA to DFA and finding the maximum number of states in an equivalent minimized DFA.

NFA to DFA Conversion:

- To convert NFA to DFA, we need to follow the subset construction algorithm. In this algorithm, we consider each state of the DFA as a set of NFA states.
- Initially, the start state of the DFA is the epsilon closure of the start state of the NFA.
- Then, for each input symbol, we find the set of states reachable from the current state of DFA by that input symbol. This set becomes the next state of the DFA.
- We repeat this process for all the states of the DFA until we get all the possible states.

Minimization of DFA:

- After converting NFA to DFA, we need to minimize the DFA to get an equivalent DFA with the minimum number of states.
- We use the state minimization algorithm to minimize the DFA. In this algorithm, we merge the states of the DFA which are equivalent, i.e., they have the same set of outgoing transitions for all input symbols.

Maximum Number of States in Minimized DFA:

- The maximum number of states in an equivalent minimized DFA can be found using the Myhill-Nerode theorem.
- According to this theorem, the number of states in a minimized DFA is at least equal to the number of distinct equivalence classes of strings in the language of the NFA.
- The number of distinct equivalence classes of strings in the language of the NFA is equal to 2^N, where N is the number of states in the NFA.
- Therefore, the maximum number of states in an equivalent minimized DFA is 2^N.

Conclusion:

Hence, we can conclude that the maximum number of states in an equivalent minimized DFA is at least 2^N.