On the State Complexity of Closures and Interiors of Regular Languages with Subwords

We study the state complexity of the set of subwords and superwords of regular languages, and provide new lower bounds in the case of languages over a two-letter alphabet. We also consider the dual interior sets, for which the nondeterministic state complexity has a doubly-exponential upper bound. We prove a matching doubly-exponential lower bound for downward interiors in the case of an unbounded alphabet.

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