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From: joes <noreply@example.com>
Newsgroups: comp.theory
Subject: Re: Can D simulated by H terminate normally?
Date: Thu, 2 May 2024 21:51:34 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Thu, 02 May 2024 12:45:44 -0500 schrieb olcott:

> On 5/2/2024 4:07 AM, Alan Mackenzie wrote:
>> olcott <polcott333@gmail.com> wrote:
>>> On 4/29/2024 1:19 PM, Alan Mackenzie wrote:

>> I think it much more likely that there's no such thing as a "simulating
>> termination analyzer".

> When a simulating termination analyzer matches one of three non-halting
> behavior patterns (a) Simple Infinite loop (b) Simple Infinite Recursion
> (c) Simple Recursive Simulation
> 
> It aborts it simulation and reports that the input specifies a
> non-halting sequence of configurations. Otherwise it continues to
> simulate the input to completion. Non-terminating inputs that have
> complex non-halting behaviors are outside of its domain.
> 
> The difference is that as long as a STA gets one input that halts
> correctly and one input that fails to halt correctly then it is a STA.
> An actual halt decider is required to be ALL knowing.

Oh hey, your halt decider doesn't actually decide halting for all inputs!
Now we know why it is impossible.

With that, greetings to all other comp.theorists.
--joes