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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD specifies recursive emulation to HHH and halting to HHH1
Date: Mon, 31 Mar 2025 21:57:41 -0500
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On 3/31/2025 9:48 PM, dbush wrote:
> On 3/31/2025 10:38 PM, olcott wrote:
>>
>> HHH must report on the behavior that its input
>> actually specifies. 
> 
> And the input specifies an algorithm that halts when executed directly.
> 

Which is NOT how it is executed.
It IS executed with recursive emulation.

>> This seems way too difficult
>> for people that can only spout off words that
>> they learned by rote, with no actual understanding
>> of the underlying principles involved.
>>
>> Every actual computation can only transform input
>> finite strings into outputs. HHH does do this.
> 
> But not as per the requirements:
> 

> 
> 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
> 
> 
>>
>> The "requirements" that you mindlessly spout off
> 
> Which would make all true statements provable if they could be met.
> 
>> violate this foundational principle of functions
>> computed by Turing machines.
> 
> Which just says that no Turing machine satisfies those requirements, as 
> Linz and others proved.
> 
>>
>> int sum(int x, int y)
>> {
>>    return 5;
>> }
>>
>> sum(2,3) does not compute the sum of 2 + 3.
>>
> 
> 
> It absolutely does.  There are *NO* requirements on the implementation, 
> only the result.

Unless and algorithm transforms its inputs
into its outputs it is not a Turing computable
function.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer