Re: D simulated by H never halts no matter what H does V3 ---

On 5/5/24 12:29 PM, olcott wrote:

On 5/5/2024 10:42 AM, joes wrote:

Am Sun, 05 May 2024 09:30:20 -0500 schrieb olcott:
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On 5/5/2024 5:36 AM, Fred. Zwarts wrote:

Op 05.mei.2024 om 05:17 schreef olcott:

On 5/4/2024 9:49 PM, Richard Damon wrote:

On 5/4/24 9:30 PM, olcott wrote:

On 5/4/2024 8:05 PM, Richard Damon wrote:

On 5/4/24 8:49 PM, olcott wrote:

On 5/4/2024 7:44 PM, Richard Damon wrote:

On 5/4/24 8:20 PM, olcott wrote:

On 5/4/2024 7:07 PM, Richard Damon wrote:

On 5/4/24 7:51 PM, olcott wrote:

On 5/4/2024 6:32 PM, Richard Damon wrote:

On 5/4/24 7:01 PM, olcott wrote:

On 5/4/2024 5:36 PM, Richard Damon wrote:

On 5/4/24 6:08 PM, olcott wrote:

On 5/4/2024 4:43 PM, Richard Damon wrote:

On 5/4/24 5:18 PM, olcott wrote:

On 5/4/2024 3:40 PM, Richard Damon wrote:

On 5/4/24 2:46 PM, olcott wrote:

On 5/4/2024 12:15 PM, Richard Damon wrote:

On 5/4/24 12:31 PM, olcott wrote:

On 5/4/2024 10:52 AM, Richard Damon wrote:

On 5/4/24 10:48 AM, olcott wrote:

On 5/4/2024 9:39 AM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 5/4/2024 5:56 AM, Alan Mackenzie wrote:

[ Followup-To: set ]

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In comp.theory olcott <polcott333@gmail.com>
wrote:

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[please snip your replies a little]
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Note, you CAN'T just "Stipulate" that a given machine IS a UTM except
by defining that it works just like a UTM, which means, for one
thing, it can NEVER abort its simulation, not even after determining
that it will simulate this input forever.
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None-the-less a TM that correctly simulates N steps cannot be said to
have simulated those N steps incorrectly on the basis that it could
have simulated N+1 steps.
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Those N steps were simulated correctly, but the fact that it stops
after N steps make it an incorrect simulation.

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In other words a decider is wrong unless it never stops simulating an
non-halting input?

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Correct. Simulating here means producing the exact same behaviour.
If it is correct up to a point, it might still make a mistake later.
The only way to know is to keep simulating.
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 void Infinite_Recursion(u32 N)
{
   Infinite_Recursion(N);
}
 It is counter-factual that the above must be infinitely
simulated to correctly determine that it never halts.
 

No, it doesn't need to be simulated forever to determine that it doesn't halt.
But, H needs to be able to show that if this EXACT input was given to a UTM simulator that will not stop until it reaches the end will not reach an end to be able to correctly say the input is non-halting.
That works with Infinite_Recursion and Infinite_Simulation, but NOT for a program that calls H, since H doesn't UNCONDITIONALLY simulate its input.