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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: DDD specifies recursive emulation to HHH and halting to HHH1
Date: Sat, 29 Mar 2025 19:46:34 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 29 Mar 2025 14:22:31 -0500 schrieb olcott:
> On 3/29/2025 2:06 PM, dbush wrote:
>> On 3/29/2025 3:03 PM, olcott wrote:
>>> On 3/29/2025 10:23 AM, dbush wrote:
>>>> On 3/29/2025 11:12 AM, olcott wrote:
>>>>> On 3/28/2025 11:00 PM, dbush wrote:
>>>>>> On 3/28/2025 11:45 PM, olcott wrote:
>>>>>>>
>>>>>>> It defines that it must compute the mapping from the direct
>>>>>>> execution of a Turing Machine
No. The mapping *to*.

>>>>>> Which does not require tracing an actual running TM, only mapping
>>>>>> properties of the TM described.
>>>>>
>>>>> The key fact that you continue to dishonestly ignore is the concrete
>>>>> counter-example that I provided that conclusively proves that the
>>>>> finite string of machine code input is not always a valid proxy for
>>>>> the behavior of the underlying virtual machine.
No, it is a confirmation of the impossibility of a halt decider.

>>>> In other words, you deny the concept of a UTM, which can take a
>>>> description of any Turing machine and exactly reproduce the behavior
>>>> of the direct execution.
>>>
>>> I deny that a pathological relationship between a UTM and its input
>>> can be correctly ignored.
It isn't being ignored. You are saying the direct execution is wrong.

>> In such a case, the UTM will not halt, and neither will the input when
>> executed directly.
> 
> It is not impossible to adapt a UTM such that it correctly simulates a
> finite number of steps of an input.
There goes universality.

-- 
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.