I'm stuck with another homework question - "Design an NFA with $n$ states such that the corresponding equivalent DFA constructed using the subset-construction method has less than $n$ states."
What I have learnt is that using subset (or powerset) construction, you can convert a given NFA with $n$ states to it's equivalent DFA with atmost $2^n$ states. I've tried constructing NFA's and tried converting them to check their equivalent DFA's number of states, with multiple attempts, but in vain.
The above question tackles the possibility of a DFA having less than equivalent states to it's corresponding NFA. The question, as mentioned in some comments, doesn't take into account the fact that a DFA can have multiple equivalent NFAs, and also suggests the solution of having unreachable states to solve the problem.
Now, this does offer a solution to my homework problem, as the given problem doesn't specify that I shouldn't use unreachable states. Regarding epsilon moves, I believe my professor mentioned not to use them, if not said in the question, or indicated as an option to use, in the given question. Regardless, I can solve my problem by adding unreachable states. But that is not my question, here.
My question is, given an arbitrary NFA with $n$ states, to begin with. (without $\epsilon$ moves or unreachable states). Is there any specific case, where the NFA (please provide an example) under said conditions is such that I can use subset construction and get a DFA with less than $n$ states?