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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: embedded_H applied to =?UTF-8?B?4p+oxKTin6kg4p+oxKTin6k=?=
Date: Mon, 29 Jul 2024 20:08:44 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Mon, 29 Jul 2024 11:16:13 -0500 schrieb olcott:
> On 7/28/2024 3:02 AM, Mikko wrote:
>> On 2024-07-27 14:08:10 +0000, olcott said:
>>> On 7/27/2024 2:21 AM, Mikko wrote:
>>>> On 2024-07-26 14:08:11 +0000, olcott said:
>>>>> On 7/26/2024 3:45 AM, Mikko wrote:
>>>>>> On 2024-07-24 13:33:55 +0000, olcott said:
>>>>>>> On 7/24/2024 3:57 AM, Mikko wrote:
>>>>>>>> On 2024-07-23 13:31:35 +0000, olcott said:
>>>>>>>>> On 7/23/2024 1:32 AM, 0 wrote:
>>>>>>>>>> On 2024-07-22 13:46:21 +0000, olcott said:
>>>>>>>>>>> On 7/22/2024 2:57 AM, Mikko wrote:
>>>>>>>>>>>> On 2024-07-21 13:34:40 +0000, olcott said:
>>>>>>>>>>>>> On 7/21/2024 4:34 AM, Mikko wrote:
>>>>>>>>>>>>>> On 2024-07-20 13:11:03 +0000, olcott said:
>>>>>>>>>>>>>>> On 7/20/2024 3:21 AM, Mikko wrote:
>>>>>>>>>>>>>>>> On 2024-07-19 14:08:24 +0000, olcott said:

>>>>>>>>>>>>> (b) We know that a decider is not allowed to report on the
>>>>>>>>>>>>> behavior computation that itself is contained within.
>>>>>>>>>>>>
>>>>>>>>>>>> No, we don't. There is no such prohibition.

>>>>>>>>>>> Another different TM can take the TM description of this
>>>>>>>>>>> machine and thus accurately report on its actual behavior.
>>>>>>>>>> If a Turing machine can take a description of a TM as its input
>>>>>>>>>> or as a part of its input it can also take its own description.
>>>>>>>>>> Every Turing machine can be given its own description as input
>>>>>>>>>> but a Turing machine may interprete it as something else.
>>>>>>>>>>
>>>>>>>>> In this case we have two x86utm machines that are identical
>>>>>>>>> except that DDD calls HHH and DDD does not call HHH1.
>>>>>>>>
>>>>>>>> That DDD calls HHH and DDD does not call HHH1 is not a difference
>>>>>>>> between two unnamed turing machines.
>>>>>>>>
>>>>>>> The same thing happens at the Peter Linz Turing Machine level I
>>>>>>> will provide that more difficult example if and only if you prove
>>>>>>> that you understand this one.
Way to disgruntle your "reviewers".

>>>>>> However, Peter Linz does not call taht same thing a difference.

>>>> Some of the properties you assert exsit actually do exist, some
>>>> don't.

>>> (a) Ĥ copies its input ⟨Ĥ⟩
>>> (b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>>> (c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
>>> (d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩
>>> (e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>>> (f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
>>> (g) goto (d) with one more level of simulation
>>> You are supposed to evaluate the above as a contiguous sequence of
>>> moves such that non-halting behavior is identified.
>> 
>> The above is an obvious tight loop of (d), (e), (f), and (g).
>> Its relevance (it any) to the topic of the discussion is not obvious.
>> 
> When we compute the mapping from the input to embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
> to the behavior specified by this input we know that embedded_H is
> correct to transition to Ĥ.qn.
> Everyone say no, no that it not the behavior of the computation that
> embedded_H is contained within: Ĥ applied to ⟨Ĥ⟩.
> It is not supposed to be (or allowed to be) the behavior of the
> executing Turing machine that embedded_H is contained within.
> It is only supposed to be the behavior that the input to embedded_H
> specifies and this includes recursive simulation.
From the fact that the simulation is recursive we know that the
embedded H is the same as the outer one.

-- 
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.