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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions apply finite string
 transformations to inputs
Date: Tue, 6 May 2025 22:22:21 -0400
Organization: i2pn2 (i2pn.org)
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On 5/6/25 11:03 AM, olcott wrote:
> On 5/6/2025 3:24 AM, Mikko wrote:
>> On 2025-05-06 02:32:01 +0000, olcott said:
>>
>>> On 5/5/2025 8:19 PM, Richard Damon wrote:
>>>> On 5/4/25 8:35 PM, olcott wrote:
>>>>> On 5/4/2025 5:34 PM, Mr Flibble wrote:
>>>>>> On Sun, 04 May 2025 23:30:54 +0100, Richard Heathfield wrote:
>>>>>>
>>>>>>> On 04/05/2025 23:15, olcott wrote:
>>>>>>>> On 5/4/2025 2:21 PM, Richard Heathfield wrote:
>>>>>>>>> On 04/05/2025 18:55, olcott wrote:
>>>>>>>>>> Changing my words then rebutting these changed words is 
>>>>>>>>>> dishonest.
>>>>>>>>>>
>>>>>>>>>> Functions computed by Turing Machines require INPUTS and produce
>>>>>>>>>> OUTPUTS DERIVED FROM THESE INPUTS.
>>>>>>>>>
>>>>>>>>> Counter-example: a Turing Machine can calculate pi without any 
>>>>>>>>> input
>>>>>>>>> whatsoever.
>>>>>>>>>
>>>>>>>>> As Mikko rightly said: a Turing machine does not need to 
>>>>>>>>> require an
>>>>>>>>> input.
>>>>>>>>>
>>>>>>>>>
>>>>>>>> IT IS NOT COMPUTING FUNCTION THEN
>>>>>>>
>>>>>>> Quoth Alan Turing:
>>>>>>>
>>>>>>> (viii) The limit of a computably convergent sequence is computable.
>>>>>>>
>>>>>>>   From (viii) and TT— 4(1—i-|--i—...) we deduce that TT is 
>>>>>>> computable.
>>>>>>>
>>>>>>> No input required.
>>>>>>>
>>>>>>>> IT IS NOT COMPUTING FUNCTION THEN IT IS NOT COMPUTING FUNCTION 
>>>>>>>> THEN IT
>>>>>>>> IS NOT COMPUTING FUNCTION THEN
>>>>>>>>
>>>>>>>> Computable functions are the basic objects of study in 
>>>>>>>> computability
>>>>>>>> theory. Computable functions are the formalized analogue of the
>>>>>>>> intuitive notion of algorithms, in the sense that 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
>>>>>>>
>>>>>>> That's a very second-rate summary of computability. Turing was 
>>>>>>> far more
>>>>>>> interested in whether a computation was possible than whether it 
>>>>>>> needed
>>>>>>> inputs. Do most computations need inputs? Most useful ones that 
>>>>>>> we care
>>>>>>> about, sure. But all? By no means.
>>>>>>>
>>>>>>>> *Computer science is ONLY concerned with computable functions*
>>>>>>>
>>>>>>> Computer science is concerned with the Halting Problem.
>>>>>>> The Halting Problem is concerned with an incomputable function.
>>>>>>> Therefore computer science is concerned with at least one 
>>>>>>> incomputable
>>>>>>> function.
>>>>>>
>>>>>> The function is neither computable nor incomputable because there 
>>>>>> is no
>>>>>> function at all, just a category error.
>>>>>>
>>>>>> /Flibble
>>>>>
>>>>> You can look at it that way or you can look
>>>>> at it as simulating termination analyzer HHH(DD)
>>>>> does correctly determine that DD cannot possibly
>>>>> reach its own final state, thus is correctly
>>>>> rejected as non-halting.
>>>>>
>>>>
>>>> Except that isn't the question that is being asked.
>>>>
>>>> In fact, that question has a trivial answer, as we can make an H0 
>>>> that just aborts its emulation and returns 0 and it is correct by 
>>>> your definition,
>>>
>>> No that is stupidly wrong as I have said at least 100 times recently.
>>> The termination analyzer must compute the mapping from the input
>>> on the basis of the behavior that this input actually specifies.
>>
>> You often say so and you often say otherwise. More specifically, you
>> have said that is correct to call the actual input non-halting if a
>> hypothetical non-decider would correctly decide that a hypthetical
>> input would not halt.
>>
> 
> <MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
>      If simulating halt decider H correctly simulates its
>      input D until H correctly determines that its simulated D
>      *would never stop running unless aborted* then
> 
>      H can abort its simulation of D and correctly report that D
>      specifies a non-halting sequence of configurations.
> </MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
> 
> *would never stop running unless aborted*
> looks at the actual input D and reports on the basis
> of a hypothetical H/D pair where H does not abort.
> 
> int DD()
> {
>    int Halt_Status = HHH(DD);
>    if (Halt_Status)
>      HERE: goto HERE;
>    return Halt_Status;
> }
> 
> _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]
> 
> DD emulated by HHH according to the rules of the
> x86 language cannot possibly reach past its own
> machine address [0000213c].
> 
> 

The problem is HHH doesn't do that, and you are caught in a lie.

DD emulated by a correct emulator according to those rules DOES halt, as 
your  HHH(DD) returns 0.