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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Wed, 7 May 2025 08:17:36 -0000 (UTC)
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Am Tue, 06 May 2025 21:40:14 -0500 schrieb olcott:
> On 5/6/2025 6:00 PM, Richard Damon wrote:
>> On 5/6/25 1:54 PM, olcott wrote:
>>> On 5/6/2025 6:06 AM, Richard Damon wrote:
>>>> On 5/5/25 10:29 PM, olcott wrote:
>>>>> On 5/5/2025 8:06 PM, Richard Damon wrote:
>>>>>> On 5/5/25 11:51 AM, olcott wrote:

>>>>>>> When HHH computes the mapping from *its input* to the behavior of
>>>>>>> DD emulated by HHH this includes HHH emulating itself emulating
>>>>>>> DD. This matches the infinite recursion behavior pattern.
>>>>>>>
>>>>>> And *ITS INPUT*, for the HHH that answers 0, is the representation
>>>>>> of a program
>>>>>
>>>>> Not at all. This has always been stupidly wrong.
>>>>> The input is actually a 100% perfectly precise sequence of steps.
>>>>> With pathological self-reference some of these steps are inside the
>>>>> termination analyzer.
>>>>>
>>>> Can't be, as the input needs to be about a program, which must, by
>>>> the definition of a program, include all its algorithm.
>>>> Yes, there are steps that also occur in the termination analyzer, but
>>>> they have been effectively copied into the program the input
>>>> describes.

>>>> What you forget is that the input program INCLUDES as its definiton,
>>>> all of the code it uses, and thus the call to the decider it is built
>>>> on includes that code into the decider, and that is a FIXED and
>>>> DETERMINDED version of the decider, the one that THIS version of the
>>>> input is designed to make wrong.
>>>> This doesn't change when you hypothosize a different decider looking
>>>> at THIS input.
>>>>
>>> *would never stop running unless aborted*
>>> Refers to a hypothetical HHH/DD pair of the same HHH that DD calls
>>> except that this hypothetical HHH never aborts.
>>>
>> Right, but a correct simulation of D does halt,
A correct simulation is one that produces the same behaviour as the
direct execution. HHH does not.

> How the Hell is breaking the rules specified by the x86 language
> possibly correct?
The rule that you may not abort? The rule that you may not simulate
hypothetical code?

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.