Re: Turing Machine computable functions apply finite string transformations to inputs

On 4/28/25 11:01 AM, olcott wrote:

On 4/28/2025 2:33 AM, Richard Heathfield wrote:

On 28/04/2025 07:46, Fred. Zwarts wrote:
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So we agree that no algorithm exists that can determine for all possible inputs whether the input specifies a program that (according to the semantics of the machine language) halts when directly executed.
Correct?

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Correct. We can, however, construct such an algorithm just as long as we can ignore any input we don't like the look of.
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 The behavior of the direct execution of DD cannot be derived
by applying the finite string transformation rules specified
by the x86 language to the input to HHH(DD). This proves that
this is the wrong behavior to measure.

Sure they can. That is what direct execution DOES.
What makes you think they can't be?
You keep on making this LYING CLAIM, and can't actually prove it, because you just are too ignorant about the rules you are talking about.
The problem is that HHH can't do that, as if it tries to be a correct emulator, and fully obey the transformation rules, it gets stuck being non-halting, because the DD that calls it in THAT case is non-halting.

 It is the behavior THAT IS derived by applying the finite
string transformation rules specified by the x86 language
to the input to HHH(DD) proves that THE EMULATED DD NEVER HALTS.

But for any HHH that transforms DD -> 0, the transforms defined by the full definition of the x86 language, which *IS* what happens when you directly execute it, it to reach the final state and halt.

 

Similarly, we can construct a list that contains all possible real numbers just as long as we can ignore any iffy numbers that smell a funny colour.
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