Re: A computable function that reports on the behavior of its actual self is not allowed

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Sujet : Re: A computable function that reports on the behavior of its actual self is not allowed
De : polcott333 (at) *nospam* gmail.com (olcott)
Groupes : comp.theory sci.logic
Date : 13. May 2024, 00:21:09
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v1rfcn$311mk$1@dont-email.me>
References : 1 2 3
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On 5/12/2024 4:40 PM, Richard Damon wrote:
On 5/12/24 5:18 PM, olcott wrote:
On 5/12/2024 2:27 PM, olcott wrote:
Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that a function is
computable if there exists an algorithm that can do the job of the
function, i.e. given an input of the function domain it can return the
corresponding output. https://en.wikipedia.org/wiki/Computable_function
>
A computable function that reports on the behavior of its actual
self (or reports on the behavior of its caller) is not allowed.
>
A decider must halt whereas simulating a pathological input
that would never halt unless aborted can only halt by aborting.
>
This causes the direct execution of this input after it has been aborted
to have different behavior than the simulated input that cannot possibly
stop running unless aborted.
>
>
*MORE PRECISE WORDING* (this may take a few more rewrites)
When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>
It is a verified fact that the directly executed Ĥ ⟨Ĥ⟩ cannot possibly
stop running unless simulating partial halt decider embedded_H aborts
its simulation of its input.
 But since embedded_H implements a specific algorithm, either it will or it won't. "unless" is a meaningless word here, it implies a case that can't happen.
 We can look at the two possible cases.
 First, if embedded_H doesn't ever abort its simulation, then, as you have desceribed, THAT embedded_H creates a H^ that will never halt, but the H that was based on will also never abort its simulation (or you lied that embedded_H is the needed copy of H) and thus never answer and fail to be a decider.
 
It can answer without halting by transitioning to its own internal
non-final state of embedded_H.qn without ever reaching Ĥ.qn. Every
simulated instance of embedded_H would do this same thing and then
continue simulating its input.
In this case embedded_H <is> an actual UTM that has the extra
feature of examining all of the state transitions of its input
to see what we can all see that Ĥ ⟨Ĥ⟩ remains stuck in recursive
simulation.
*Or we can get an actual partial halt decider as follows*
*Or we can get an actual partial halt decider as follows*
*Or we can get an actual partial halt decider as follows*
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.
*THIS MAKES THE BEHAVIOR OF THE DIRECT*
*EXECUTION AN INCORRECT MEASURE IN THIS CASE*
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Date Sujet#  Auteur
12 May 24 * A computable function that reports on the behavior of its actual self is not allowed42olcott
12 May 24 +- Re: A computable function that reports on the behavior of its actual self is not allowed1Richard Damon
12 May 24 +* Re: A computable function that reports on the behavior of its actual self is not allowed19olcott
12 May 24 i`* Re: A computable function that reports on the behavior of its actual self is not allowed18Richard Damon
13 May 24 i `* Re: A computable function that reports on the behavior of its actual self is not allowed17olcott
13 May 24 i  `* Re: A computable function that reports on the behavior of its actual self is not allowed16Richard Damon
13 May 24 i   +* Re: A computable function that reports on the behavior of its actual self is not allowed6olcott
13 May 24 i   i`* Re: A computable function that reports on the behavior of its actual self is not allowed5Richard Damon
13 May 24 i   i `* Re: A computable function that reports on the behavior of its actual self is not allowed4olcott
13 May 24 i   i  `* Re: A computable function that reports on the behavior of its actual self is not allowed3Richard Damon
13 May 24 i   i   `* Re: A computable function that reports on the behavior of its actual self is not allowed2olcott
14 May 24 i   i    `- Re: A computable function that reports on the behavior of its actual self is not allowed1Richard Damon
13 May 24 i   `* Re: A computable function that reports on the behavior of its actual self is not allowed9olcott
13 May 24 i    +* Re: A computable function that reports on the behavior of its actual self is not allowed5Richard Damon
13 May 24 i    i`* Re: A computable function that reports on the behavior of its actual self is not allowed4olcott
13 May 24 i    i `* Re: A computable function that reports on the behavior of its actual self is not allowed3Richard Damon
13 May 24 i    i  `* Re: A computable function that reports on the behavior of its actual self is not allowed2olcott
14 May 24 i    i   `- Re: A computable function that reports on the behavior of its actual self is not allowed1Richard Damon
13 May 24 i    `* Re: A computable function that reports on the behavior of its actual self is not allowed3joes
13 May 24 i     `* Re: A computable function that reports on the behavior of its actual self is not allowed2olcott
14 May 24 i      `- Re: A computable function that reports on the behavior of its actual self is not allowed1Richard Damon
13 May 24 +- Re: A computable function that reports on the behavior of its actual self is not allowed1Mikko
13 May 24 +* Re: A computable function that reports on the behavior of its actual self is not allowed19Fred. Zwarts
13 May 24 i`* Re: A computable function that reports on the behavior of its actual self is not allowed18olcott
13 May 24 i +* Re: A computable function that reports on the behavior of its actual self is not allowed9Fred. Zwarts
13 May 24 i i`* Re: A computable function that reports on the behavior of its actual self is not allowed8olcott
13 May 24 i i +* Re: A computable function that reports on the behavior of its actual self is not allowed6Fred. Zwarts
13 May 24 i i i`* Re: A computable function that reports on the behavior of its actual self is not allowed5olcott
13 May 24 i i i `* Re: A computable function that reports on the behavior of its actual self is not allowed4Fred. Zwarts
13 May 24 i i i  `* Re: A computable function that reports on the behavior of its actual self is not allowed3olcott
13 May 24 i i i   `* Re: A computable function that reports on the behavior of its actual self is not allowed2Fred. Zwarts
13 May 24 i i i    `- Re: A computable function that reports on the behavior of its actual self is not allowed1olcott
14 May 24 i i `- Re: A computable function that reports on the behavior of its actual self is not allowed1Richard Damon
13 May 24 i +* Re: A computable function that reports on the behavior of its actual self is not allowed7immibis
14 May 24 i i`* Re: A computable function that reports on the behavior of its actual self is not allowed6olcott
14 May 24 i i +- Re: A computable function that reports on the behavior of its actual self is not allowed1Richard Damon
14 May 24 i i `* Re: A computable function that reports on the behavior of its actual self is not allowed4immibis
14 May 24 i i  `* Re: A computable function that reports on the behavior of its actual self is not allowed +++3olcott
14 May 24 i i   +- Re: A computable function that reports on the behavior of its actual self is not allowed +++1wij
14 May 24 i i   `- Re: A computable function that reports on the behavior of its actual self *is* allowed +++1Richard Damon
14 May 24 i `- Re: A computable function that reports on the behavior of its actual self is not allowed1Richard Damon
13 May 24 `- Re: A computable function that reports on the behavior of its actual self is not allowed1olcott

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