Re: Halting Problem: What Constitutes Pathological Input

On 5/5/2025 6:29 PM, olcott wrote:

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.
 

None-the-less you have agreed on many occasions that the theorem which the halting problem proofs prove is correct.