Re: HHH(DD) --- COMPUTE ACTUAL MAPPING FROM INPUT TO OUTPUT --- Using Finite String Transformations

On 23/04/2025 10:02, Fred. Zwarts wrote:

Op 22.apr.2025 om 21:50 schreef olcott:

On 4/22/2025 2:30 PM, Fred. Zwarts wrote:

Op 22.apr.2025 om 21:14 schreef olcott:

On 4/22/2025 1:10 PM, Fred. Zwarts wrote:

Op 22.apr.2025 om 18:38 schreef olcott:

>
a function is computable if there exists an algorithm
that can do the job of the function, i.e. given an input
of the function domain it can return the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
>
On Turing Machines inputs <are> finite strings, and
finite string transformation rules <are> applied to
these finite strings to derive corresponding outputs.
>

And it has been proven that no finite string transformations are possible that report the halting behaviour for all inputs that specify a correct program.

>
int sum(int x, int y) { return x + y; }
Only when people stupid assume the same thing as
sum(3,2) should return the sum of 5 + 3.
>

Therefore HHH should report on the actual input, the finite string that describes a halting program. Not on the hypothetical input that does not halt, because it is based on a hypothetical HHH that does not abort.
>
Why do you maintain that HHH should process the hypothetical input instead of the actual input.
Do you really believe that 3+2 equals 5+3?

>
I have proven that the directly executed DD and DD
emulated by HHH according to the semantics of the
x86 language have a different set of state changes
many hundreds of times for several years.

You never showed a proof. You only repeated a dream. You are dreaming many years without any logic. You failed to show the first state change where the direct execution is different from the simulation. You only showed an erroneous HHH that fails to reach the end of the simulation of a halting program.

Worse than this, on more than one occasion I've actually posted traces of computation DDD(DDD) executed directly and simulated by HHH side by side.  Both traces were of course /identical/, up to the point where HHH stops simulating.  I even compared (but did not post) the /full/ traces including instructions outside of DDD which PO normally suppresses.  This makes the trace quite long - tens of thousands of entries as I recall - but as expected they were identical line for line right up to the point where HHH aborts the trace.
This feature of computation, namely that every computation has exactly one defined sequence of computation steps is perhaps THE most basic feature of computation, capturing its essential notion. It's understood by students even before they turn up for the first lecture introducing the definition of a TM.  I dare say it's understood by children who've never heard of a TM, but understand what an algorithm is, or broadly what a "computer program" is, or who have sat through one of those school lessons where they are presented with a simple flow chart to calculate something.
PO seems unable to take this on board mentally.  I'd guess he understands at some level that if his claim that "the trace depends on who is doing the simulation" is revealed as nonsense, then his claim that HHH is "correct" when it gives the wrong answer collapses, and in fact must be viewed as laughable.  He would have to admit he has simply wasted 20 years (or whatever) of his life on something that was Plain Wrong.
PO's response to these posts is to ignore them - it's like he's been shell shocked, and like a childhood trauma he suppresses the memory of the event.  After a couple of weeks he just starts repeating the claim that he has proved the traces differ and that it is a "verified fact" etc., as though nothing has happened.  (Of course the truth is the exact opposite - the verified fact is that the traces are identical up to the point where HHH decides to stop the simulation.)
Mike.