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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: No decider is accountable for the computation that itself is
 contained within
Date: Tue, 30 Jul 2024 21:09:09 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Tue, 30 Jul 2024 15:13:34 -0500 schrieb olcott:
> On 7/30/2024 2:52 PM, joes wrote:
>> Am Tue, 30 Jul 2024 11:24:35 -0500 schrieb olcott:
>>> On 7/30/2024 2:24 AM, joes wrote:
>>>> Am Mon, 29 Jul 2024 15:32:44 -0500 schrieb olcott:
>>>>> On 7/29/2024 3:17 PM, joes wrote:
>>>>>> Am Mon, 29 Jul 2024 11:32:00 -0500 schrieb olcott:
>>>>>>> On 7/28/2024 3:40 AM, Mikko wrote:
>>>>>>>> On 2024-07-27 14:21:50 +0000, olcott said:
>>>>>>>>> On 7/27/2024 2:46 AM, Mikko wrote:
>>>>>>>>>> On 2024-07-26 16:28:43 +0000, olcott said:
>>>>
>>>>>>> Halt deciders are not allowed to report on the behavior of the
>>>>>>> actual computation that they themselves are contained within. They
>>>>>>> are only allowed to compute the mapping from input finite strings.
>>>>>> What if the input is the same as the containing computation?
>>>>> It always is except in the case where the decider is reporting on
>>>>> the TM description that itself is contained within.
>>>
>>>> I don't understand. "The input is not the same as the containing
>>>> computation when deciding on the description of the containing
>>>> computation"?
>> I mean: is that an accurate paraphrase?
>> 
>>> An executing Turing machine is not allowed to report on its own
>>> behavior. Every decider is only allowed to report on the behavior that
>>> its finite string input specifies.
>> And what happens when those are the same?
> That is always the case except in the rare exception that I discovered
> where a simulating halt decider is simulating the input that calls
> itself.
Always? Most TMs don't get themselves as input. OTOH that is one of
the most interesting cases.
The description of a TM specifies the behaviour of that machine
when it is running.

-- 
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.