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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD simulated by HHH cannot possibly halt (Halting Problem) ---
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Date: Mon, 14 Apr 2025 18:14:53 -0400
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On 4/14/2025 5:43 PM, olcott wrote:
> On 4/14/2025 6:52 AM, dbush wrote:
>> On 4/14/2025 7:46 AM, olcott wrote:
>>>
>>> Such an HHH works fine when the input DD is not attempting
>>> to do the opposite of whatever this HHH reports. This is not
>>> a problem though. DD merely changes its own behavior through
>>> the pathological self-reference that it implements.
>>
>> Category error. DD is an algorithm, i.e. a fixed immutable sequence of 
>> instructions, therefore "changing its behavior" is impossible.  It 
>> only does exactly what its instructions say.
>>
> 
> One version of DD is defined to screw with HHH.

More precisely with *algorithm* HHH.  Remember, DD is an algorithm 
consisting of the fixed code of the function DD, the fixed code of the 
function HHH, and the fixed code of everything that function HHH calls 
down to the OS level.

Likewise, algorithm HHH consists of the function HHH and everything that 
function HHH calls down to the OS level.

If you change any of that, even hypothetically, you're changing the 
input and no longer talking about algorithm DD.

Changing the input is not allowed.

> 
>>>
>>> Then HHH simply reports on this changed behavior. HHH need not
>>> even know that DD is calling itself. It only need to know that
>>> the behavior of DD would prevent its own termination.
>>>
>>
>> In other words, HHH is changing the input and reporting on the changed 
>> input.
>>
>> Changing the input is not allowed.
>>
> 
>