Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: =?UTF-8?Q?Re=3A_Flibble=E2=80=99s_Leap=3A_Why_Behavioral_Divergence?=
 =?UTF-8?Q?_Implies_a_Type_Distinction_in_the_Halting_Problem?=
Date: Sun, 11 May 2025 18:14:56 -0500
Organization: A noiseless patient Spider
Lines: 39
Message-ID: <vvrb1g$me5h$2@dont-email.me>
References: <vv1UP.77894$JJT6.54808@fx16.ams4> <vvqd4u$g8a1$1@dont-email.me>
 <7N2UP.527443$wBt6.464256@fx15.ams4> <vvqfgq$gmmk$1@dont-email.me>
 <os3UP.670056$BFJ.223954@fx13.ams4> <vvqgpt$gmmk$4@dont-email.me>
 <aG3UP.366972$wBVe.321504@fx06.ams4> <vvqhaj$gldn$6@dont-email.me>
 <bV3UP.101097$0ia.1168@fx11.ams4> <vvqkff$gldn$13@dont-email.me>
 <WH4UP.229898$_Npd.172992@fx01.ams4> <vvqm03$i3hn$1@dont-email.me>
 <g55UP.688178$4AM6.545580@fx17.ams4>
 <87o6vy4ulc.fsf@nosuchdomain.example.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Mon, 12 May 2025 01:14:57 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="15cac720ddbb61c7f6586fe023932af8";
	logging-data="735409"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/Kg8hTLA4Y5TXd8A9RiyFm"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:H49+tOkkSk0GpSOUippd3GVboiE=
X-Antivirus-Status: Clean
X-Antivirus: Norton (VPS 250511-4, 5/11/2025), Outbound message
In-Reply-To: <87o6vy4ulc.fsf@nosuchdomain.example.com>
Content-Language: en-US
Bytes: 3198

On 5/11/2025 6:05 PM, Keith Thompson wrote:
> Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
>> On Sun, 11 May 2025 18:15:47 +0100, Richard Heathfield wrote:
>>
>>> On 11/05/2025 17:59, Mr Flibble wrote:
>>>> it is impossible to obtain a halting result
>>>
>>>
>>> That sure looks like a concession that it's impossible to devise an
>>> algorithm that will produce a halting result.
>>>
>>> Well done. We got you there in the end.
>>
>> No. The reason why it is impossible to obtain a halting result for
>> pathological input is not the reason proposed by Turing (i.e. self-
>> referential diagonalization), it is impossible to obtain a halting result
>> for pathological input because the self-referential conflation of decider
>> and input is a category error that prevents us from performing
>> diagonalization.
> 
> Is it possible to determine whether a given input is "pathological" or not?
> 
>> To usefully advance research in this area pathological input needs to be
>> excluded from the set of programs that can be analysed by a decider.
> 
> Can this exclusion be performed reliably and consistently?
> 

That is a good question. The answer is definitely
yes. When HHH emulates DDD it only needs to see
that DDD is calling itself with no conditional branch
instructions inbetween.

Whether a function computed by a Turing machine can
do this is a different question.

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