On 9/2/2021 11:59 PM, André G. Isaak wrote:
> On 2021-09-02 22:09, olcott wrote:
>> On 9/2/2021 10:52 PM, Richard Damon wrote:
>>> On 9/2/21 11:18 PM, olcott wrote:
>
>>>> Any input that never halts unless its simulation is aborted is an input
>>>> that never halts.
>>>>
>>>
>>> Bad Terminology. Inputs themselves don't halt. They only represent
>>> computations that might be halting or not.
>>>
>>
>>     In computability theory, the halting problem is the
>>     problem of determining, from a description of an arbitrary
>>     computer program and an input, whether the program will
>>     finish running, or continue to run forever.
>>     https://en.wikipedia.org/wiki/Halting_problem
>>
>> To bypass the pathology of pathological inputs:
>>     In computability theory, the halting problem is the
>>     problem of determining, from a description of an arbitrary
>>     computer program and an input,
>>
>>     whether the simulation of this input must be aborted to
>>     prevent it from running forever.
>>
>> The above criteria is valid on the basis of the known equivalence
>> between the direct execution of a computation and its simulation by a
>> UTM. The same criteria universally works on all inputs.
>
> But the direct execution of P(P) *does* halt. So if there is an
> equivalence between direct execution and simulation by a UTM, then the
> simulation by a UTM must also halt.
>
> André
>

The direct execution of P has a dependency on the H(P,P) that it calls.
int main(){ P(P); } only halts because its call to H(P,P) returns 0. No
instance of H(P,P) has any dependency on the return value of another
function.

This makes int main(){ P(P); } a computationally distinct different
computation than H(P,P) that has no such dependency.

You can dance all around this yet there exists no correct rebuttal in
the universe that shows that these computations are equivalent or that
computations that are not equivalent must have equivalent behavior.

In computability theory, the halting problem is the
problem of determining, from a description of an arbitrary
computer program and an input, whether the program will
finish running, or continue to run forever.
https://en.wikipedia.org/wiki/Halting_problem

To bypass the pathology of pathological inputs:
In computability theory, the halting problem is the
problem of determining, from a description of an arbitrary
computer program and an input,

whether the simulation of this program must be aborted to
prevent it from running forever.

The above criteria is valid on the basis of the known equivalence
between the direct execution of a computation and its simulation
by a UTM. The same criteria universally works on all inputs allowing
their halting status to be correctly decided.

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein