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From: joes <noreply@example.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: A computable function that reports on the behavior of its actual
 self is not allowed
Date: Mon, 13 May 2024 08:22:19 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sun, 12 May 2024 18:19:12 -0500 schrieb olcott:
> On 5/12/2024 5:40 PM, Richard Damon wrote:
>> On 5/12/24 6:21 PM, olcott wrote:

>>> No decider is ever allowed to report on its own behavior thus
>>> embedded_H as a simulating partial halt decider is NOT ALLOWED to
>>> report on the direct execution of Ĥ ⟨Ĥ⟩ because this IS REPORTING ON
>>> ITS OWN BEHAVIOR.
>> 
>> WHO SAYS THIS?
> 
> A decider must compute the mapping from an input.
> Its actual self cannot possibly be an input.
Oh, it definitely can. It must decide for every machine, including
itself. How would you even detect that?

> No decider takes an actual Turing machine as input thus no decider can
> possibly take its actual self as input.
Well, an encoding of one.

> (a) The behavior of the directly executed Ĥ ⟨Ĥ⟩ is after embedded_H ⟨Ĥ⟩
> ⟨Ĥ⟩ has already aborted its simulation.
> 
> (b) The behavior of the simulated input to embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
> is before embedded_H has aborted its simulation.
> 
> (c) These two behaviors (a) and (b) ARE NOT THE SAME. (a) will stop
> running on its own (b) will never stop running unless aborted.
Then they are either not the same machine, or simulated incorrectly.

-- 
joes