Are there Non-Regular Languages?

Here we investigate the question of whether there exist non-regular languages by looking at a different question: if a "long" string in a DFA is accepted, can we infer any other information about other strings in the DFA also being accepted?
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I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.

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