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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Every sufficiently competent C programmer knows --- Semantic
 Property of Finite String
Date: Wed, 12 Mar 2025 18:36:19 -0400
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On 3/12/2025 6:31 PM, olcott wrote:
> On 3/12/2025 5:03 PM, dbush wrote:
>> On 3/12/2025 5:38 PM, olcott wrote:
>>> On 3/12/2025 3:53 PM, dbush wrote:
>>>> On 3/12/2025 4:29 PM, olcott wrote:
>>>>> On 3/12/2025 2:16 PM, dbush wrote:
>>>>>> On 3/11/2025 10:46 PM, olcott wrote:
>>>>>>> On 3/11/2025 9:41 PM, dbush wrote:
>>>>>>>> On 3/11/2025 10:39 PM, olcott wrote:
>>>>>>>>> On 3/11/2025 9:37 PM, dbush wrote:
>>>>>>>>>> On 3/11/2025 10:36 PM, olcott wrote:
>>>>>>>>>>> On 3/11/2025 9:32 PM, dbush wrote:
>>>>>>>>>>>> On 3/11/2025 10:31 PM, olcott wrote:
>>>>>>>>>>>>> On 3/11/2025 9:18 PM, dbush wrote:
>>>>>>>>>>>>>> On 3/11/2025 10:06 PM, olcott wrote:
>>>>>>>>>>>>>>> On 3/11/2025 9:02 PM, dbush wrote:
>>>>>>>>>>>>>>>> On 3/11/2025 9:41 PM, Richard Heathfield wrote:
>>>>>>>>>>>>>>>>> On 12/03/2025 01:22, olcott wrote:
>>>>>>>>>>>>>>>>>> DDD correctly simulated by HHH never reaches its
>>>>>>>>>>>>>>>>>> own "return" instruction and terminates normally
>>>>>>>>>>>>>>>>>> in any finite or infinite number of correctly
>>>>>>>>>>>>>>>>>> simulated steps.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> If it correctly simulates infinitely many steps, it 
>>>>>>>>>>>>>>>>> doesn't terminate. Look up "infinite".
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> But your task is to decide for /any/ program, not just 
>>>>>>>>>>>>>>>>> DDD. That, as you are so fond of saying, is 
>>>>>>>>>>>>>>>>> 'stipulated', and you can't get out of it. The whole 
>>>>>>>>>>>>>>>>> point of the Entscheidungsproblem is its universality. 
>>>>>>>>>>>>>>>>> Ignore that, and you have nothing.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Given that his code has HHH(DD) returning 0, 
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> THESE ARE THE WORDS ANYONE THAT DODGES THESE
>>>>>>>>>>>>>>> WORDS WILL BE TAKEN FOR A LIAR
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> void DDD()
>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>    HHH(DDD);
>>>>>>>>>>>>>>>    return;
>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> DDD correctly simulated by HHH never reaches its
>>>>>>>>>>>>>>> own "return" instruction and terminates normally
>>>>>>>>>>>>>>> in any finite or infinite number of correctly
>>>>>>>>>>>>>>> simulated steps.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Changing the input is not allowed.
>>>>>>>>>>>>>
>>>>>>>>>>>>> *You are simply lying that any input was ever changed*
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> You did precisely that when you hypothesize different code 
>>>>>>>>>>>> for HHH.
>>>>>>>>>>>>
>>>>>>>>>>>> Changing the input is not allowed.
>>>>>>>>>>>
>>>>>>>>>>> *THIS IS WHAT MY ORIGINAL WORDS MEANT*
>>>>>>>>>>> HHH is the infinite set of every possible C function
>>>>>>>>>>> that correctly emulates N steps of its input where
>>>>>>>>>>> N any finite positive integer.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> In other words, you're changing the input.
>>>>>>>>>>
>>>>>>>>>> Changing the input is not allowed.
>>>>>>>>>
>>>>>>>>> It is an infinite set of HHH/DDD pairs having the
>>>>>>>>> property that DDD[0] ... DDD[N] never halts.
>>>>>>>>>
>>>>>>>>
>>>>>>>> In other words, you're not answering the question that a 
>>>>>>>> solution to the halting problem is required to answer:
>>>>>>>>
>>>>>>>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when 
>>>>>>>> executed directly
>>>>>>>>
>>>>>>>
>>>>>>> Yes I am yet you refuse to pay anywhere near close
>>>>>>> enough attention to see how I already fully addressed this.
>>>>>>> If you pay 100% perfect attention you might get it.
>>>>>>>
>>>>>>
>>>>>> False.  (<DDD>,null) maps to 1 as per the above requirements, but 
>>>>>> your HHH maps (<DDD>,null) to 0, therefore it fails to meet the 
>>>>>> requirements.
>>>>>
>>>>> <unrelated copy-paste response>
>>>>>
>>>>
>>>>
>>>> So no response?  I'll take it that you agree with the above.
>>>
>>> Making sure to always give credit where credit is due this
>>> point in our conversation is the point where I first translated
>>> my perspective into the semantic property of a finite string.
>>>
>>> A decider is required to report on a semantic (or syntactic)
>>> property of its input finite string (even if Rice incorrectly
>>> says this is impossible in this case) and not allowed to report
>>> on any damn thing else.
>>>
>>> The fact that DDD calls HHH(DDD) in recursive emulation
>>> <is> an aspect of the semantics of the input finite string
>>> that cannot be correctly ignored.
>>>
>>>
>>
>> Remember the stipulative definition of a solution to the halting problem:
>>
>>
> 
> Is to map the input finite string to the semantic property
> of this finite string. Any other mapping contradicts the
> definition of a decider.

And that property is as follows:

(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly

I should also point out that I never mentioned anything about a 
"decider", simply "a solution to the halting problem".  Neither did Linz.