Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Functions computed by Turing Machines MUST apply finite string
 transformations to inputs --- MT
Date: Wed, 7 May 2025 14:55:22 -0400
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On 5/7/2025 2:47 PM, olcott wrote:
> On 5/7/2025 10:44 AM, joes wrote:
>> Am Wed, 07 May 2025 10:03:55 -0500 schrieb olcott:
>>> On 5/7/2025 7:01 AM, dbush wrote:
>>>> On 5/7/2025 6:16 AM, Fred. Zwarts wrote:
>>>>> Op 06.mei.2025 om 21:15 schreef olcott:
>>
>>>>>> None-the-less it is the words that the best selling author of theory
>>>>>> of computation textbooks agreed to: *would never stop running unless
>>>>>> aborted*
>>>>>> is the hypothetical HHH/DD pair where the same HHH that DD calls does
>>>>>> not abort the simulation of its input.
>>>>>>
>>>>> Nevertheless, this change makes it fundamentally different.
>>>>> I can't believe that you are so stupid to think that modifying a
>>>>> program does not make a program different. Are you trolling?
>>>>
>>>> Given that he's shown he doesn't understand (and this list is by no
>>>> means exhaustive):
>>>> * what requirements are * what correct means * what true means * what a
>>>> proof is * how proof by contradiction works
>>>> I wouldn't put it past him that he actually believes it.  He'll say
>>>> anything to avoid admitting to himself that he wasted that last 22
>>>> years not understanding what he was working on.
>>>> (Anyone else that wants to add to this list, feel free)
>>>
>>> A simulating halt decider must correctly predict *what the behavior
>>> would be* if it did not abort its simulation.
> 
>> ...if it, the simulator, didn't abort. The input DD that is being
>> simulated still calls the same real HHH that does abort.
> HHH needs to predict what would happen if this very same
> HHH did not abort its input.

Category error.  Algorithms do one thing and one thing only.  There's no 
such thing as "what if an algorithm did something else".  That's just a 
different algorithm.

To satisfy the below requirements, HHH must predict what would happen in 
the hypothetical case that DD is executed directly, or alternately what 
would happen in the hypothetical case that DD is simulated by UTM.


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