Re: Functions computed by Turing Machines MUST apply finite string transformations to inputs +++

On 5/4/25 12:06 PM, olcott wrote:

On 5/3/2025 4:28 PM, dbush wrote:

On 5/3/2025 3:45 PM, Richard Heathfield wrote:

>
I am conscious that you have already explained to me (twice!) that Mr O's approach is aimed not at overturning the overarching indecidability proof but a mere detail of Linz's proof. Unfortunately, your explanations have not managed to establish a firm root in what passes for my brain. This may be because I'm too dense to grok them, or possibly it's because your explanations are TOAST (see above).
>
You have said, I think, that Olcott doesn't need a universal decider in order to prove his point. But a less ambitious decider doesn't contradict Linz's proof, surely? So once more for luck, what exactly would PO be establishing with his non-universal and impatient simulator if he could only get it to work?

>
The core issue is that PO, despise being nearly 70 and having worked as a programmer, fundamentally doesn't understand proof by contradiction.
>

 The actual issue is the NO ONE here (or perhaps anywhere)
sufficiently understands the key details about
COMPUTING THE MAPPING FROM AN INPUT TO AN OUTPUT.

No, the problem is you don't understand is that the mapping that the halt decider is being asked to compute, doesn't need to be defined by a "computation".

 Many here know that a mapping from the input must be
computed. What they don't know are ALL of the tiny
detailed steps required to compute this mapping.

No, it doesn't. The DECIDER can only do a computation, but the mapping it is asked to compute doesn't need to be.
Please try to show a reference that says a "Function" (not a "Computable Function") has to have its mapping computed.
Of that we can only create problems based on Computable Funcitons.

 They simply guess that because DD(DD) halts that
DD correctly simulated by HHH must also halt.

No, the problem is that HHH doesn't correctlyu simulate its input.
A fact you have implicitly agreed to by refusing to show where the so called "correct simulation" by HHH actually correctly diviated from that actual correct simulation that matched the direct execution of the input.
You know, the instruction correctly simulated according to the x86 language as described by the official Intel Documentation.

 They cannot provide these detailed steps of the
execution trace of each machine instruction showing
exactly how DD correctly emulated by HHH halts
BECAUSE THEY KNOW THAT THEY ARE WRONG AND ONLY PLAYING HEAD GAMES.

Because you have proven that no HHH that answer can correctly simulate its input.
In fact, your asking for someone to provide your proof just shows you don't understand how proofs actualy worl.

 _DD()
[00002133] 55         push ebp      ; housekeeping
[00002134] 8bec       mov ebp,esp   ; housekeeping
[00002136] 51         push ecx      ; make space for local
[00002137] 6833210000 push 00002133 ; push DD
[0000213c] e882f4ffff call 000015c3 ; call HHH(DD)
[00002141] 83c404     add esp,+04
[00002144] 8945fc     mov [ebp-04],eax
[00002147] 837dfc00   cmp dword [ebp-04],+00
[0000214b] 7402       jz 0000214f
[0000214d] ebfe       jmp 0000214d
[0000214f] 8b45fc     mov eax,[ebp-04]
[00002152] 8be5       mov esp,ebp
[00002154] 5d         pop ebp
[00002155] c3         ret
Size in bytes:(0035) [00002155]
 

Which isn't a correct program, as it doesn't include to code for HHH, and if you do include the code of your Halt7.c, your requirement becomes a category error as you can't aslk for the results of a correct simulation from a defined program that does do one.
All you are showing is you fundamentally don't understand what a "Program", is, showing you are just totally ignorant of what you talk about.