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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Correcting the definition of the halting problem --- Computable
 functions
Date: Tue, 25 Mar 2025 21:19:06 -0400
Organization: i2pn2 (i2pn.org)
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On 3/25/25 10:49 AM, olcott wrote:
> On 3/25/2025 4:22 AM, Mikko wrote:
>> On 2025-03-25 03:29:06 +0000, olcott said:
>>
>>> 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>
>>
>> There are computable functions that take Turing machines as arguments.
>> For example, the number of states of a Turing machine.
>>
>> The computability of a function requires that the domain can be mapped
>> to finite strings.
>>
> 
> IT IS COUNTER-FACTUAL THAT A MACHINE DESCRIPTION SPECIFIES
> BEHAVIOR IDENTICAL TO THE DIRECTLY EXECUTED MACHINE.

Why? Since that *IS* the definition for a Halt Decider.

> 
> _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]
> 
> When any finite number of steps of III is emulated by
> EEE according to the semantics of the x86 language the
> emulated III never reaches its "ret" instruction final
> halt state and the directly executed III does halt.
> 
> This conclusively proves that a machine description does
> not always specify the same behavior as the directly
> executed machine.
> 

Nope, it might say that for a POOP decider it doesn't, but partial 
emulation of other inputs means nothing in a discussion of Halt Deciders.

Your problem is you just refuse to learn the meaning of the words you 
use, so you just turn yourself into a pathological liar with a total 
disregard for the actual truth,

Sorry, you have sunk your repuation in that lake of fire, and will 
likely be joining it soon.