Re: Halting Problem: What Constitutes Pathological Input

On 5/6/2025 5:57 PM, Richard Damon wrote:

On 5/6/25 5:56 PM, olcott wrote:

On 5/6/2025 4:12 PM, dbush wrote:

On 5/6/2025 4:57 PM, olcott wrote:

On 5/6/2025 3:49 PM, dbush wrote:

On 5/6/2025 4:37 PM, olcott wrote:

On 5/6/2025 3:22 PM, joes wrote:

Am Tue, 06 May 2025 13:05:15 -0500 schrieb olcott:

On 5/6/2025 5:59 AM, Richard Damon wrote:

On 5/5/25 10:18 PM, olcott wrote:

On 5/5/2025 8:59 PM, dbush wrote:

On 5/5/2025 8:57 PM, olcott wrote:

On 5/5/2025 7:49 PM, dbush wrote:

>

DO COMPUTE THAT THE INPUT IS NON-HALTING IFF (if and only if) the
mapping FROM INPUTS IS COMPUTED.

i.e. it is found to map something other than the above function
which is a contradiction.

The above function VIOLATES COMPUTER SCIENCE. You make no attempt to
show how my claim THAT IT VIOLATES COMPUTER SCIENCE IS INCORRECT you
simply take that same quote from a computer science textbook as the
infallible word-of-God.

What does it violate?
>

All you are doing is showing that you don't understand proof by
contradiction,

Not at all. The COMPUTER SCIENCE of your requirements IS WRONG!

No, YOU don't understand what Computer Science actually is talking
about.

Every function computed by a model of computation must apply a specific
sequence of steps that are specified by the model to the actual finite
string input.

>

You are very confused. An algorithm or program computes a function.
>

>
Nothing computes a function unless it applies a specific
set of rules to its actual input to derive its output.
Anything that ignores its input is not computing a function.
>

>
False.  Anything that correctly associates a function's input to a function's output for all elements of the function's domain does in fact compute that function.
>
>
For example, given this function:
>
For all integers X and Y:
(X,Y) maps to 5
>
This algorithm computes it:
>
int foo(int X, int Y) { return 5; }
>

>
The rules that must be applied to the inputs
are

>
Anything that can associate the input with the output.
>

>
WRONG!
Any defined process that CAUSES an INPUT to be associated
with an OUTPUT.
>

 And it does, it causes ALL inputs to be associated with the value 5.

Ignoring the input cannot possibly be construed
as computing the mapping from the input.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer