Re: Halting Problem: What Constitutes Pathological Input

On 5/6/25 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 the rules of arithmetic. Since the input
was ignored foo() did not compute the sum
of any input. INPUTS must be transformed into
OUTPUTS using rules.

What rules said the method that must be used to get the answer?
The rules of the mapping define a way to get the correct answer, not the only way to determine it.

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

In other words you are admitting that you are just lying about everythinng you said being applicable to the actual problems since you are just talking about Olcott-Prorgramms which no one cares about, and you probably can't actually define.

 INPUTS must correspond to OUTPUTS.
There must be some process that ensures that
INPUTS correspond to OUTPUTS. Every process
must have some sequence of steps.
 

So?
That doesn't seem to be that different from what classical theory defines as a computation in a computational model.
Your problem is you confuse that with the mappings that Computations are trying to compute to be correct.
And return 5, *IS* a sequence of steps, perhaps of just length 1.