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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: The philosophy of computation reformulates existing ideas on a new basis ---
Date: Thu, 31 Oct 2024 12:49:24 +0200
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On 2024-10-29 14:35:34 +0000, olcott said:

> On 10/29/2024 2:57 AM, Mikko wrote:
>> On 2024-10-29 00:57:30 +0000, olcott said:
>> 
>>> On 10/28/2024 6:56 PM, Richard Damon wrote:
>>>> On 10/28/24 11:04 AM, olcott wrote:
>>>>> On 10/28/2024 6:16 AM, Richard Damon wrote:
>>>>>> The machine being used to compute the Halting Function has taken a 
>>>>>> finite string description, the Halting Function itself always took a 
>>>>>> Turing Machine,
>>>>>> 
>>>>> 
>>>>> That is incorrect. It has always been the finite string Turing Machine
>>>>> description of a Turing machine is the input to the halt decider.
>>>>> There are always been a distinction between the abstraction and the
>>>>> encoding.
>>>> 
>>>> Nope, read the problem you have quoted in the past.
>>>> 
>>> 
>>> Ultimately I trust Linz the most on this:
>>> 
>>> the problem is: given the description of a Turing machine
>>> M and an input w, does M, when started in the initial
>>> configuration qow, perform a computation that eventually halts?
>>> https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf
>>> 
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>> 
>>> Linz also makes sure to ignore that the behavior of ⟨Ĥ⟩ ⟨Ĥ⟩
>>> correctly simulated by embedded_H cannot possibly reach
>>> either ⟨Ĥ.qy⟩ or ⟨Ĥ.qn⟩ because like everyone else he rejects
>>> simulation out of hand:
>>> 
>>> We cannot find the answer by simulating the action of M on w,
>>> say by performing it on a universal Turing machine, because
>>> there is no limit on the length of the computation.
>> 
>> That statement does not fully reject simulation but is correct in
>> the observation that non-halting cannot be determied in finite time
>> by a complete simulation so someting else is needed instead of or
>> in addition to a partial simulation. Linz does include simulationg
>> Turing machines in his proof that no Turing machine is a halt decider.
>> 
> 
> *That people fail to agree with this and also fail to*
> *correctly point out any error seems to indicate dishonestly*
> *or lack of technical competence*
> 
> DDD emulated by HHH according to the semantics of the x86
> language cannot possibly reach its own "return" instruction
> whether or not any HHH ever aborts its emulation of DDD.

- irrelevant
- couterfactual

-- 
Mikko