Path: ...!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: No decider is accountable for the computation that itself is
 contained within
Date: Mon, 29 Jul 2024 15:32:44 -0500
Organization: A noiseless patient Spider
Lines: 47
Message-ID: <v88u9c$kpv7$1@dont-email.me>
References: <v80irs$2tlb5$1@dont-email.me> <v828ju$3a1gf$1@dont-email.me>
 <v82vpu$3dftr$6@dont-email.me> <v8506m$3s27b$1@dont-email.me>
 <v88g60$i7kl$5@dont-email.me>
 <8ac9fd02d6247cec58098de53c964a5feed41946@i2pn2.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 29 Jul 2024 22:32:45 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="9d358cc663705f17d44fb4afa23cd753";
	logging-data="681959"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+OnLma1L65iwAFiIRx5LIg"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:ngzoGZFNPwnV9h6k/AQN8gZ4zMA=
Content-Language: en-US
In-Reply-To: <8ac9fd02d6247cec58098de53c964a5feed41946@i2pn2.org>
Bytes: 3151

On 7/29/2024 3:17 PM, joes wrote:
> Am Mon, 29 Jul 2024 11:32:00 -0500 schrieb olcott:
>> On 7/28/2024 3:40 AM, Mikko wrote:
>>> On 2024-07-27 14:21:50 +0000, olcott said:
>>>> On 7/27/2024 2:46 AM, Mikko wrote:
>>>>> On 2024-07-26 16:28:43 +0000, olcott said:
>>>>>
>>>>>> No decider is ever accountable for the behavior of the computation
>>>>>> that itself is contained within.
>>>>> That claim is fully unjustified. How do you even define "accountable"
>>> in the context of computations, automata, and deciders?
> 
>> Halt deciders report the halt status on the basis of the behavior that a
>> finite string input specifies.
> Which is constructed to be the same as the surrounding computation.
> 
>> Did you think that halt deciders report the halt status on some other
>> basis?
> No, what do you think the basis was?
> 
>> Halt deciders are not allowed to report on the behavior of the actual
>> computation that they themselves are contained within. They are only
>> allowed to compute the mapping from input finite strings.

> What if the input is the same as the containing computation?
> 

It always is except in the case where the decider
is reporting on the TM description that itself is
contained within.

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

(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

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