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Yes, since "the first, the middle, and the last characters of $w$ are identical" is not really well defined here (so there might be ambiguities like is $\epsilon\in L$?) Probably it wont really matter for the question if you assume $\epsilon\in L$ or $\epsilon \notin L$ (other than some small change in the PDA or CFG) But if you really want to make sure ...


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Your problem is NP-hard. To see this, you can reduce it from the minimum test cover (or test collection) problem: given a set $X$ of $\ell$ elements and a collection $C = \{C_1, \dots, C_k \}$ of $k$ subsets of $X$, find a minimum test cover for $X$ and $C$, i.e., a subset $C'$ of $C$ that has minimum size and satisfies the following property: for every pair ...


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Note the following line of code: powerSet.add(new ArrayList<>(SelectedSoFar); Whenever we create a subset, we add the subset (list) to a list of list : power set. The size of subset will be $n$ (actually it will vary from $1$ to $n$, but we can take it to be $n$). Even though adding a list requires one line of code, but it will involve copying all ...


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