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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Correcting the definition of the halting problem --- Computable functions
Date: Tue, 25 Mar 2025 10:54:35 +0200
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On 2025-03-24 16:44:52 +0000, olcott said:

> On 3/24/2025 10:14 AM, dbush wrote:
>> On 3/24/2025 11:03 AM, olcott wrote:
>>> On 3/24/2025 6:23 AM, Richard Damon wrote:
>>>> On 3/23/25 11:09 PM, olcott wrote:
>>>>> It is impossible for HHH compute the function from the direct
>>>>> execution of DDD because DDD is not the finite string input
>>>>> basis from which all computations must begin.
>>>>> https://en.wikipedia.org/wiki/Computable_function
>>>> 
>>>> WHy isn't DDD made into the correct finite string?i
>>>> 
>>> 
>>> DDD is a semantically and syntactically correct finite
>>> stirng of the x86 machine language.
>> 
>> Which includes the machine code of DDD, the machine code of HHH, and 
>> the machine code of everything it calls down to the OS level.
>> 
>>> 
>>>> That seems to be your own fault.
>>>> 
>>>> The problem has always been that you want to use the wrong string for 
>>>> DDD by excluding the code for HHH from it.
>>>> 
>>> 
>>> DDD emulated by HHH directly causes recursive emulation
>>> because it calls HHH(DDD) to emulate itself again. HHH
>>> complies until HHH determines that this cycle cannot
>>> possibly reach the final halt state of DDD.
>>> 
>> 
>> Which is another way of saying that HHH can't determine that DDD halts 
>> when executed directly.
>> 
> 
> given an input of the function domain it can
> return the corresponding output.
> https://en.wikipedia.org/wiki/Computable_function
> 
> Computable functions are only allowed to compute the
> mapping from their input finite strings to an output.

A comutable function does not compute. A Turing machine can compute
a value of a computable function.

All computations are allowed. There are not other restrictions on
computable functions that that it must be a function and thane it
must be computable.

-- 
Mikko