Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions apply finite string
 transformations to inputs
Date: Tue, 6 May 2025 10:03:52 -0500
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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].


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer