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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Halting Problem: What Constitutes Pathological Input
Date: Mon, 5 May 2025 17:29:42 -0500
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On 5/5/2025 5:00 PM, dbush wrote:
> On 5/5/2025 5:40 PM, Richard Heathfield wrote:
>> On 05/05/2025 22:31, dbush wrote:
>>> It's just that no algorithm exists that can compute that mapping, as 
>>> proven by Linz and other and as you have *explicitly* agreed is correct.
>>
>> He's coming round to the idea, albeit slowly. He can't bring himself 
>> to describe the mapping as 'incomputable' or 'undecidable', but he's 
>> started to claim that such a mapping is 'incorrect', which is a tacit 
>> acknowledgement that it exists.
>>
> 
> Oh, he's agreed to it many times.  Here's a partial list:
> 
> 
> On 3/24/2025 10:07 PM, olcott wrote:
>  > A halt decider cannot exist
> 
> On 4/28/2025 2:47 PM, olcott wrote:
>  > On 4/28/2025 11:54 AM, dbush wrote:
>  >> And the halting function below is not a computable function:
>  >>
>  >
>  > It is NEVER a computable function
>  >
>  >> 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
> 
> On 3/14/2025 1:19 PM, olcott wrote:
>  > When we define the HP as having H return a value
>  > corresponding to the halting behavior of input D
>  > and input D can actually does the opposite of whatever
>  > value that H returns, then we have boxed ourselves
>  > in to a problem having no solution.
> 
> On 6/21/2024 1:22 PM, olcott wrote:
>  > the logical impossibility of specifying a halt decider H
>  > that correctly reports the halt status of input D that is
>  > defined to do the opposite of whatever value that H reports.
>  > Of course this is impossible.
> 
> On 7/4/2023 12:57 AM, olcott wrote:
>  > If you frame the problem in that a halt decider must divide up finite
>  > strings pairs into those that halt when directly executed and those that
>  > do not, then no single program can do this.
> 
> On 5/5/2025 5:39 PM, olcott wrote:
>  > On 5/5/2025 4:31 PM, dbush wrote:
>  >> Strawman.  The square root of a dead rabbit does not exist, but the
>  >> question of whether any arbitrary algorithm X with input Y halts when
>  >> executed directly has a correct answer in all cases.
>  >>
>  >
>  > It has a correct answer that cannot ever be computed
> 
> 

There never has been any input that could
ever actually do the opposite of whatever
value that its termination analyzer returns.
That part of its code was ALWAYS unreachable.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer