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Old 05-23-2019, 02:04 PM
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Originally Posted by wolfpup View Post
It depends on what question you're asking. If you're concerned about whether a device is Turing equivalent, you need to understand what it's actually doing. But when computation is viewed simply as the output of a black box, it's always reducible to the mapping of a set of input symbols to a set of output symbols. So I take the view that any black box that deterministically produces such a mapping for all combinations of inputs has to be regarded as ipso facto computationally equivalent to any other that produces the same mapping, without reference to what's going on inside it. Of course, the mechanisms involved may be trivial, like a simple table lookup, that may not provide any insights into the nature of computation and may not be Turing equivalent.
In the real world this is an important problem. We need to prove that the implementation of a specification is equivalent to the specification. It turns out that this is basically impossible without being able to see the inside of the black box, even for large systems without internal memory, and practically impossible for those with memory.
Of course you have to agree on the input and output symbols, and they must be consistent across computational systems. This doesn't seem to be a requirement for HMHW's view of interpretation.
In other words, Lincoln was wrong - a horse does have five legs if you interpret the tail as a leg.