Path: nntp.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: My reviewers think that halt deciders must report on the behavior
 of their caller
Date: Thu, 17 Jul 2025 08:31:32 -0500
Organization: A noiseless patient Spider
Lines: 47
Message-ID: <105atvk$1bk0p$2@dont-email.me>
References: <101nq32$99vd$1@dont-email.me> <104fduv$2n8gq$2@dont-email.me>
 <4cb5d16be8d1e6549823f35081050e7dad462da2@i2pn2.org>
 <104gi8j$2uc68$2@dont-email.me>
 <152859a4a4ef31aa45580e873eb6970c34b97ef9@i2pn2.org>
 <104hmb5$35gkb$1@dont-email.me>
 <f12be9e3474cf08b01ae1a4381f77205bbac1da3@i2pn2.org>
 <104i15g$36mma$2@dont-email.me>
 <c0cf1db3b26b15b6b2df8a22e9f415c10aee59a7@i2pn2.org>
 <104jcqn$3jrpl$10@dont-email.me> <104lb03$13ioh$2@dont-email.me>
 <104lp8o$7l4q$7@dont-email.me> <104o662$18h8g$1@dont-email.me>
 <104oj2v$t0u4$7@dont-email.me> <104qimm$1dpnl$1@dont-email.me>
 <104rad9$1icss$3@dont-email.me> <104t4na$21rg3$1@dont-email.me>
 <104tra1$264oq$2@dont-email.me> <104vm2f$2ldm1$1@dont-email.me>
 <1050in9$2qkok$3@dont-email.me> <1052gji$3au6g$1@dont-email.me>
 <105304j$3dptv$3@dont-email.me> <105567k$5rd$1@dont-email.me>
 <1055kg7$2t13$6@dont-email.me> <1057pe1$l9av$1@dont-email.me>
 <1058fn9$pn5l$2@dont-email.me> <105a9r1$18s08$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Thu, 17 Jul 2025 15:31:33 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="757a756c4546e5542c44a33ac5ff5463";
	logging-data="1429529"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19o4aaGl3nLwbl5yIdqiyDi"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:dsM2O4UObIshbCjyumRnDUcBIQk=
In-Reply-To: <105a9r1$18s08$1@dont-email.me>
Content-Language: en-US
X-Antivirus-Status: Clean
X-Antivirus: Norton (VPS 250717-2, 7/17/2025), Outbound message

On 7/17/2025 2:47 AM, Mikko wrote:
> On 2025-07-16 15:15:53 +0000, olcott said:
> 
>> On 7/16/2025 3:55 AM, Mikko wrote:
>>>
>>> If there were an error in the proof you would quote the erronoeus 
>>> inference.
>>
>> The error is the requirement that a halt decider
>> reports on the direct execution of a machine that
>> is not an input.
> 
> That was stimpluated before asking the question that the proof answers.
> 

No Turing Machine decider can ever report on the
behavior of anything that is not an input encoded
as a finite string.

*From the bottom of page 319 has been adapted to this*
https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf

Ĥ is not a finite string input to Ĥ.embedded_H
⟨Ĥ⟩ ⟨Ĥ⟩ are finite string inputs to Ĥ.embedded_H

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞
     ⟨Ĥ⟩ ⟨Ĥ⟩ simulated by Ĥ.embedded_H reaches
     its simulated final halt state of ⟨Ĥ.qn⟩, and

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
     ⟨Ĥ⟩ ⟨Ĥ⟩ simulated by Ĥ.embedded_H cannot possibly
     reach its simulated final halt state of ⟨Ĥ.qn⟩.

When Ĥ is applied to ⟨Ĥ⟩ and embedded_H is a
simulating partial halt decider
(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 until
embedded_H sees the repeating pattern and transitions to Ĥ.qn.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer