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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 18:03:04 -0400
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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:


Given any algorithm (i.e. a fixed immutable sequence of instructions) X 
described as <X> with input Y:

A solution to the halting problem is an algorithm H that computes the 
following mapping:

(<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


The description of the algorithm is something that is set and fixed, and 
so doesn't depend on how a potential solution is implemented.

In this case, <DDD> i.e. the description of the algorithm defined by the 
function DDD, the function HHH, and everything it calls down to the OS 
level is stipulated to be the address of the function DDD.  Again, this 
description is constant.

This means that when DDD is passed to HHH, for HHH to meet the above 
requirements it must to compute the mapping for (<DDD>,null) which is 1. 
  It maps this to 0 is it fails to meet the above requirements for a 
solution to the halting problem.

Again, the implementation of HHH has nothing to do with the description 
given to it or the required mapping.