Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Turing computable functions
Date: Tue, 25 Mar 2025 17:02:38 -0400
Organization: A noiseless patient Spider
Lines: 53
Message-ID: <vrv5le$3hle3$12@dont-email.me>
References: <vruvsn$3tamc$3@dont-email.me> <vrv0d4$3hle3$10@dont-email.me>
 <vrv18e$3tamc$4@dont-email.me> <vrv2aa$3hle3$11@dont-email.me>
 <vrv4up$3t3k$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 25 Mar 2025 22:02:38 +0100 (CET)
Injection-Info: dont-email.me; posting-host="558cb3f1e92ebc1bf3f45b6c0d288267";
	logging-data="3724739"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19yjNmIaVpgvTEVYU7j8QPy"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:flMRGaEZypgfsSsPab0iMBrg6UA=
In-Reply-To: <vrv4up$3t3k$1@dont-email.me>
Content-Language: en-US
Bytes: 2884

On 3/25/2025 4:50 PM, olcott wrote:
> On 3/25/2025 3:05 PM, dbush wrote:
>> On 3/25/2025 3:47 PM, olcott wrote:
>>> On 3/25/2025 2:32 PM, dbush wrote:
>>>> On 3/25/2025 3:24 PM, olcott wrote:
>>>>> Cannot possibly derive any outputs not computed from
>>>>> their inputs.
>>>>
>>>> Correct, algorithms can only compute computable mathematical function.
>>>>
>>>>>
>>>>> A Turing machine halt decider 
>>>>
>>>> Does not exist because the required mapping is not computable:
>>>>
>>>>
>>>> Given any algorithm (i.e. a fixed immutable sequence of 
>>>> instructions) X described as <X> with input Y:
>>>>
>>>> A solution to the halting problem is an algorithm H that computes 
>>>> the following mapping:
>>>>
>>>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed 
>>>> directly
>>>>
>>>>
>>>>
>>>>> cannot possibly report
>>>>> on the behavior of any directly executing process.
>>>>> No Turing machine can every do this. This has always
>>>>> been beyond what any Turing machine can ever do.
>>>>
>>>>
>>>> Strawman: reporting on an executing process is not a requirement. 
>>>
>>> YOU JUST SAID THAT IT WAS
>>> YOU KEEP MINDLESSLY REPEATING THAT IT IS
>>>
>>> On 3/25/2025 2:32 PM, dbush wrote:
>>>  > (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>>>
>>>
>>
>> I never said it had to actually watch an executing process, only 
>> report what would happen if it did run.
>>
> 
> *It has been conclusively proven as a verified*
> *fact many hundreds of times over several years*
> That the behavior that the finite string input specifies

Is the behavior of directly executing the described Turing machine.