Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott2@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: =?UTF-8?B?UmU6IFZlcmlmaWVkIGZhY3QgdGhhdCDEpC5IIOKfqMSk4p+pIOKfqMSk?=
 =?UTF-8?B?4p+pIGFuZCBIIOKfqMSk4p+pIOKfqMSk4p+pIGhhdmUgZGlmZmVyZW50IGJlaGF2?=
 =?UTF-8?Q?ior?=
Date: Sat, 9 Mar 2024 16:22:18 -0600
Organization: A noiseless patient Spider
Lines: 65
Message-ID: <usineq$2hnpb$3@dont-email.me>
References: <usia2e$2f2pd$1@dont-email.me> <usijm6$1bt2h$1@i2pn2.org>
 <usikk8$2gnhr$8@dont-email.me> <usiljd$2hc10$3@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sat, 9 Mar 2024 22:22:18 -0000 (UTC)
Injection-Info: dont-email.me; posting-host="7bba1e21ad186023a2af4b4bf0f27e98";
	logging-data="2678571"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+WcfCuSnUP5MjIPZuj9nwK"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:NnVmQ+xP+l/B1MCkbLAu3X5jnrU=
In-Reply-To: <usiljd$2hc10$3@dont-email.me>
Content-Language: en-US
Bytes: 3883

On 3/9/2024 3:50 PM, immibis wrote:
> On 9/03/24 22:34, olcott wrote:
>> On 3/9/2024 3:17 PM, Richard Damon wrote:
>>> On 3/9/24 10:33 AM, olcott wrote:
>>>> *Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior*
>>>>
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>
>>> Specifications, not actual behavior until the existance of such an H 
>>> is shown.
>>>
>>> IF taken as actual behavior, then it is conditional on such an H 
>>> existing.
>>>
>>>>
>>>> Execution trace of Ĥ applied to ⟨Ĥ⟩
>>>> (a) Ĥ.q0 The input ⟨Ĥ⟩ is copied then transitions to Ĥ.H
>>>> (b) Ĥ.H applied ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy) simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>> (c) which begins at its own simulated ⟨Ĥ.q0⟩ to repeat the process
>>>> *This proves that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ must abort its simulation*
>>>
>>> It NEEDS to in order to meet its specification
>>>
>>> It DOESN'T unless its algorithm says it does,
>>>
>>> If it just fails to answer, then it has failed to be a correct Halt 
>>> Decider.
>>>
>>> The fact that you reach this conflict in actions, is the reason Halt 
>>> Deciding is uncomputable.
>>>
>>>>
>>>> *This is a verified fact*
>>>> When simulating halt deciders always report on the behavior of
>>>> their simulated input from their own POV then when Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>> transitions to Ĥ.Hqn it is correct from its own POV.
>>>
>>> In other words, you are admitting to changing the question, and thus 
>>> LYING that you are working on the actual original problem.
>>
>> This must just be over your head. It is very very difficult.
>>
>> What criteria would you use so that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ knows what
>> wrong answer to provide?
>>
> 
> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is stipulated to use the exact same objective criteria that 
> H ⟨Ĥ⟩ uses.

Simulating halt deciders must make sure that they themselves
do not get stuck in infinite execution. This means that they
must abort every simulation that cannot possibly otherwise halt.

This requires Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ to abort its simulation and does not
require H ⟨Ĥ⟩ ⟨Ĥ⟩ to abort its simulation when Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ aborts
its simulation.

Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ does simulate itself in recursive simulation H ⟨Ĥ⟩ ⟨Ĥ⟩
does not simulate itself in recursive simulation.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer