Re: Recursive simulation must be reported and not ignored.

Am Sat, 10 May 2025 20:49:55 -0500 schrieb olcott:

On 5/10/2025 8:07 PM, Richard Damon wrote:

On 5/10/25 9:00 PM, olcott wrote:

On 5/10/2025 6:56 PM, Mr Flibble wrote:

On Sat, 10 May 2025 18:40:53 -0400, Richard Damon wrote:

And the problem is that you use incorrect categories.
The decider needs to be of the category "Program".
The input also needs to be of the category "Program", but provided
via a representation. The act of representation lets us convert
items of category Program to the category of Finite String which can
be an input.

>
Those two categories you have identified are different hence the
category error.
>

That is correct. A running program and an input finite string ARE NOT
THE SAME.

 
But there is a direct relationship between the two.
 

The key thing is that they don't always have the same behavior.

A representation doesn't have any behaviour at all, the program it
represents does.

When they do have different behavior

...the direct execution can't be wrong.

It is not allowed to ignore this on the basis that the direct execution
or UTM simulation has no recursive simulation.

The direct execution has recursive simulation just the same.

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.