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Dec 3, 2013 at 17:07 comment added Jisang Yoo Somewhat similar to this answer is this: One asks "is there a regular expression for matching numbers divisible by 7?" and the answer is "Yes. Just prove that any DFA can be converted to a regular expression."
Apr 13, 2010 at 21:00 comment added Qiaochu Yuan I don't know about "needed": my understanding is that people simply didn't believe that such things were possible before Matiyasevich's theorem was proven. The actual construction was done explicitly a few years later by Jones et al.: en.wikipedia.org/wiki/…
Apr 13, 2010 at 18:27 history answered TonyK CC BY-SA 2.5