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My favourite description of a computer is a function
f(p, in) -> [out]
such that for any other function g a value of p can be found such that
f(p, in) = g(in)
If a machine can be transformed into a function f that has this quality, it is a computer.
Edit: obviously g has to be computable so the actual rule is a bit different, but the gist of it is this.
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