Can you suggest me a good book with illustrative examples and problems with solutions for finite languages and automata theory?
I tried Hopcroft's but it has mostly theory and not many problems with solutions.
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Try this question to get an idea. I think the classical ones at universities are the one from Sipser and Hopcroft's one. For Hopcroft I would really look for the old version if you are mathematically inclined. They removed a lot of proofs in new versions.
For specific examples of problems you'll get solutions here and there over the Internet. It is good not to have a straight look to the solution and having the solution very near can be very tempting at times.
While looking for books to get an idea of what's on them I like this Internet library. Then you can always buy the book on paper or borrow it from your University library.
Hope this helps.
Some books with solutions: (under construction)
Hopcroft's et alii. solutions to their book.
Apparently, Sipser's book contains solutions after each chapter.
I know its been a while since this question has been asked, but I think that Problem Solving in Automata, Languages, and Complexity by Ding Zhu Du is the best book for, surprisingly, problem solving!
It contains plentiful examples for DFA, NFA, using pumping lemma to prove irregularity, proving regularity of weird languages which seem to be irregular and complicated!
Its available as PDF for free on internet, I hope it's legal!