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Can strings with a finite length < pq (p,q are two distinct numbers) be straight away assumed to be regular as we can make a DFA for them? Also, what can be said about the set of such finite length strings?

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 Strings cannot be regular: regularity is a property of sets of strings, not strings. In any case, this question is not quite on-topic here, where the topic is math-research related subjects. Your question will better fit sites like math.stackexchange.com (or its sister CS site, I guess) – Mariano Suárez-Alvarez May 29 at 18:05
I think that some questions about automata and theory of computation are perfectly fine for this site, especially if connected with algebra or logic. However, I do agree this question is off-topic. – Benjamin Steinberg May 29 at 19:31
@benjamin, automata theory and the theory of computation are math subjects :=) – Mariano Suárez-Alvarez May 29 at 19:50

closed as off topic by Mariano Suárez-Alvarez, Steven Landsburg, Chris Godsil, Andreas Blass, Qiaochu Yuan May 29 at 20:10

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