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You can find specialized books consisting entirely or problems from particular math domains (e.g. linear algebra, polynomials, combinatorics), but I've yet to find such a book for automata of any kind.

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  • $\begingroup$ The exercises in Hopcroft & Ullman first edition, and possibly also the earlier FLRA book by them (available online at dl.acm.org/citation.cfm?id=1096945)? $\endgroup$ – András Salamon Feb 20 '14 at 22:11
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    $\begingroup$ I would like such a book, pretty sure there isn't one though. If we were to build one as a community, Shiva Kintali's site TrueShelf would be a good place to collect such problems. trueshelf.com/all $\endgroup$ – Andy Drucker Feb 20 '14 at 22:55
  • $\begingroup$ Similar question: cstheory.stackexchange.com/questions/1955/… $\endgroup$ – Sylvain Feb 21 '14 at 13:27
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    $\begingroup$ The book "Elements of Automata Theory" by Sakarovitch covers Automata Theory deeply. However, he uses a different notation compared to TCS-oriented texts. Once you got over this, its a pretty good book. $\endgroup$ – A.Schulz Mar 23 '14 at 21:47
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Sort of indirectly, this book is about research level automata problems:

http://www.amazon.ca/Automatic-Sequences-Theory-Applications-Generalizations/dp/0521823323

An automatic sequence is essentially a set of strings which can be computed by a DFA.

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