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> A striking bit of trivia (but OT to SQL) is that in Turing's "On Computable Numbers" [1] he treats a Turing Machine that halts as having a problem, whereas in
by mmarx 5y ago
> A striking bit of trivia (but OT to SQL) is that in Turing's "On Computable Numbers" [1] he treats a Turing Machine that halts as having a problem, whereas in basically every popular treatment a machine that halts is one that gives you an answer, and a machine that doesn't halt is one with a bug, like it entered an infinite loop. But his paper is the opposite (and doesn't use the word "halt" at all!):
Note that his machines compute real numbers, which always have a an infinitely long binary representation (with possibly infinitely many trailing zeroes), whereas usually one considers Turing machines computing natural numbers, which always have a finite binary representation.
- pjungwir 5y agoYes, it makes sense. But it sure took me by surprise when I finally read the original paper.