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: Correcting the definition of the halting problem --- Computable
 functions ---HHH(DD)
Date: Tue, 25 Mar 2025 13:24:43 -0400
Organization: A noiseless patient Spider
Lines: 122
Message-ID: <vruosq$3hle3$7@dont-email.me>
References: <vr1shq$1qopn$1@dont-email.me> <vrqicu$3s258$1@dont-email.me>
 <30c2beae6c191f2502e93972a69c85ff227bfd03@i2pn2.org>
 <vrrs79$11a56$7@dont-email.me> <vrrsta$tdm5$1@dont-email.me>
 <vrs264$1a43i$1@dont-email.me> <vrs54q$1d1o2$1@dont-email.me>
 <vrse90$1jr8u$1@dont-email.me> <vrsk13$1q39o$1@dont-email.me>
 <vrsn62$1rblu$2@dont-email.me> <vrsnhu$1q39o$2@dont-email.me>
 <vrsodl$1rblu$3@dont-email.me> <vrsogj$1q39o$3@dont-email.me>
 <vrsqlq$1rblu$4@dont-email.me> <vrsrmr$1q39o$4@dont-email.me>
 <vrt14i$264jb$1@dont-email.me> <vrt1tu$257a2$1@dont-email.me>
 <vrt357$264jb$2@dont-email.me> <vrt6va$22073$1@dont-email.me>
 <vrt7u2$2au0q$1@dont-email.me> <vrufj5$3hle3$1@dont-email.me>
 <vrug1b$3gia2$5@dont-email.me> <vrugj2$3hle3$3@dont-email.me>
 <vruh6d$3j3me$2@dont-email.me> <vruhf1$3hle3$4@dont-email.me>
 <vrumaj$3n7k6$1@dont-email.me> <vrumke$3hle3$5@dont-email.me>
 <vrun8e$3n7k6$2@dont-email.me> <vrunm9$3hle3$6@dont-email.me>
 <vruogg$3n7k6$3@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 18:24:43 +0100 (CET)
Injection-Info: dont-email.me; posting-host="558cb3f1e92ebc1bf3f45b6c0d288267";
	logging-data="3724739"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19HDgLEavMlJSZVCFtIMcPb"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:qZlfyHTZmKnaDW65k6U7bMBPAFg=
Content-Language: en-US
In-Reply-To: <vruogg$3n7k6$3@dont-email.me>
Bytes: 6921

On 3/25/2025 1:18 PM, olcott wrote:
> On 3/25/2025 12:04 PM, dbush wrote:
>> On 3/25/2025 12:56 PM, olcott wrote:
>>> On 3/25/2025 11:46 AM, dbush wrote:
>>>> On 3/25/2025 12:40 PM, olcott wrote:
>>>>> On 3/25/2025 10:17 AM, dbush wrote:
>>>>>> On 3/25/2025 11:13 AM, olcott wrote:
>>>>>>> On 3/25/2025 10:02 AM, dbush wrote:
>>>>>>>> On 3/25/2025 10:53 AM, olcott wrote:
>>>>>>>>> On 3/25/2025 9:45 AM, dbush wrote:
>>>>>>>>>> On 3/24/2025 11:29 PM, olcott wrote:
>>>>>>>>>>> On 3/24/2025 10:12 PM, dbush wrote:
>>>>>>>>>>>> On 3/24/2025 10:07 PM, olcott wrote:
>>>>>>>>>>>>> On 3/24/2025 8:46 PM, André G. Isaak wrote:
>>>>>>>>>>>>>> On 2025-03-24 19:33, olcott wrote:
>>>>>>>>>>>>>>> On 3/24/2025 7:00 PM, André G. Isaak wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> In the post you were responding to I pointed out that 
>>>>>>>>>>>>>>>> computable functions are mathematical objects.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Computable_function
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Computable functions implemented using models of computation
>>>>>>>>>>>>>>> would seem to be more concrete than pure math functions.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Those are called computations or algorithms, not 
>>>>>>>>>>>>>> computable functions.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Pure_function
>>>>>>>>>>>>> Is another way to look at computable functions implemented
>>>>>>>>>>>>> by some concrete model of computation.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> And not all mathematical functions are computable, such as 
>>>>>>>>>>>> the halting function.
>>>>>>>>>>>>
>>>>>>>>>>>>>> The halting problems asks whether there *is* an algorithm 
>>>>>>>>>>>>>> which can compute the halting function, but the halting 
>>>>>>>>>>>>>> function itself is a purely mathematical object which 
>>>>>>>>>>>>>> exists prior to, and independent of, any such algorithm 
>>>>>>>>>>>>>> (if one existed).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> None-the-less it only has specific elements of its domain
>>>>>>>>>>>>> as its entire basis. For Turing machines this always means
>>>>>>>>>>>>> a finite string that (for example) encodes a specific
>>>>>>>>>>>>> sequence of moves.
>>>>>>>>>>>>
>>>>>>>>>>>> False.  *All* turing machine are the domain of the halting 
>>>>>>>>>>>> function, and the existence of UTMs show that all turning 
>>>>>>>>>>>> machines can be described by a finite string.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> You just aren't paying enough attention. Turing machines
>>>>>>>>>>> are never in the domain of any computable function.
>>>>>>>>>>> <snip>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> False.  The mathematical function that counts the number of 
>>>>>>>>>> instructions in a turing machine is computable.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> It is impossible for an actual Turing machine to
>>>>>>>>> be input to any other TM.
>>>>>>>>>
>>>>>>>>
>>>>>>>> But a description of a turing machine can be, for example in the 
>>>>>>>> form of source code or a binary.  And a turing machine by 
>>>>>>>> definition *always* behaves the same for a given input when 
>>>>>>>> executing directly.
>>>>>>>
>>>>>>> IT IS COUNTER-FACTUAL THAT A MACHINE DESCRIPTION ALWAYS
>>>>>>> SPECIFIES
>>>>>>> BEHAVIOR IDENTICAL TO THE DIRECTLY EXECUTED MACHINE.
>>>>>>>
>>>>>>> _III()
>>>>>>> [00002172] 55         push ebp      ; housekeeping
>>>>>>> [00002173] 8bec       mov  ebp,esp  ; housekeeping
>>>>>>> [00002175] 6872210000 push 00002172 ; push III
>>>>>>> [0000217a] e853f4ffff call 000015d2 ; call EEE(III)
>>>>>>> [0000217f] 83c404     add  esp,+04
>>>>>>> [00002182] 5d         pop  ebp
>>>>>>> [00002183] c3         ret
>>>>>>> Size in bytes:(0018) [00002183]
>>>>>>
>>>>>> That is not the complete description.  The complete description 
>>>>>> consists of the code of III
>>>>>
>>>>> and the fact that EEE 
>>>>
>>>> Is called by III makes the code of EEE part of the fixed input, as 
>>>> well as everything that EEE calls down to the OS level.
>>>>
>>>
>>> Which is not relevant to whether or not III emulated
>>> by EEE reaches its own final halt state.
>>>
>>
>> Which is why III emulated by EEE is not relevant.
>>
> 
> When the question is:
> Does III emulated by EEE reach its final halt state
> when III defines a pathological relationship with its emulator?
> 


But that's not the question.  The question is whether or not an H exists 
that behaves as described below:


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