Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions apply finite string
 transformations to inputs VERIFIED FACT
Date: Tue, 29 Apr 2025 14:46:54 +0100
Organization: Fix this later
Lines: 44
Message-ID: <vuql8e$1svmd$1@dont-email.me>
References: <vu6lnf$39fls$2@dont-email.me> <vugddv$b21g$2@dont-email.me>
 <0a2eeee6cb4b6a737f6391c963386745a09c8a01@i2pn2.org>
 <vugvr3$pke9$8@dont-email.me>
 <4818688e0354f32267e3a5f3c60846ae7956bed2@i2pn2.org>
 <vuj18i$2lf64$6@dont-email.me>
 <f0d3f2e87d9a4e0b0f445f60a33d529f41a4fcf7@i2pn2.org>
 <vuj55m$2lf64$10@dont-email.me> <vuj8h3$2uahf$3@dont-email.me>
 <vujfuu$35hcg$1@dont-email.me>
 <65dddfad4c862e6593392eaf27876759b1ed0e69@i2pn2.org>
 <vujlj0$3a526$1@dont-email.me> <vujln7$32om9$8@dont-email.me>
 <vujmmm$3a526$2@dont-email.me> <vujmrj$32om9$9@dont-email.me>
 <vujtcb$3gsgr$1@dont-email.me> <vuju44$3hnda$1@dont-email.me>
 <vuk47o$3qkbb$1@dont-email.me> <vuk6b6$3l184$1@dont-email.me>
 <vuls34$1bf1j$4@dont-email.me> <vun87k$2m24h$2@dont-email.me>
 <vunb06$2fjjl$5@dont-email.me> <vuo57j$3h5l9$2@dont-email.me>
 <vuoath$3ljma$1@dont-email.me> <vuohgi$3td7u$1@dont-email.me>
 <vuonh6$2g74$2@dont-email.me> <vupeor$qf60$1@dont-email.me>
 <vupu0r$18vrc$1@dont-email.me> <vuqj5u$1rljg$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Tue, 29 Apr 2025 15:47:00 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="a99ce2d194518084f1e3236eb6fd133d";
	logging-data="1998541"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18eONTxILASekOXXLDvNbK0p7XaJ2JeYCQl0vkHh/xwZw=="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:3OV4Ueftg9I1y38CY1jZMt0miVo=
In-Reply-To: <vuqj5u$1rljg$1@dont-email.me>
Content-Language: en-GB

On 29/04/2025 14:11, olcott wrote:
> On 4/29/2025 2:10 AM, Richard Heathfield wrote:
>> On 29/04/2025 03:50, olcott wrote:

<snip>

>>> Yet it is H(P,D) and NOT P(D) that must be measured.
>>
>> Nothing /has/ to be measured. P's behaviour (halts, doesn't 
>> halt) when given D as input must be /established/. 
> 
> No H can possibly see the behavior of P(D)

It doesn't have to. It only has to be able to read two tapes, one 
containing P and the other containing D.

> when-so-ever D has defined a pathological
> relationship with H this changes the behavior
> of P so that it is not the same as P(D).

D has no relationship with H. D is just a list of data symbols on 
a Turing Machine tape. P, too, is a list of symbols - a program. 
You don't have to run it to read it. H's job is not to run P but 
to analyse P to determine whether P would halt if fed D as input.

The behaviour that P would exhibit if fed D is determined only by 
the symbols on the P-tape and the D-tape. H is neither here nor 
there.

If H elects to run P as part of its job, fine, but it's not 
obligatory and does not give H licence to change P, change D, or 
reject either tape. H /must/ report, correctly, for /any/ P/D 
pair. And it can't, as you rightly conceded when you wrote: 
"Computing the actual behavior the direct execution of any input 
is ALWAYS IMPOSSIBLE".

<snip>

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within