Re: Halting Problem: What Constitutes Pathological Input

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.

INPUTS must be transformed into
OUTPUTS using rules.

And the above does that.

 This is brand new computer science that I just created.
It can be inferred from the other details of what
computable functions are:
 INPUTS must correspond to OUTPUTS.

And for foo it does for the above mapping.

There must be some process that ensures that
INPUTS correspond to OUTPUTS.

And the process employed by foo does that.

Every process
must have some sequence of steps.