Re: No decider is accountable for the computation that itself is contained within

On 7/29/2024 3:17 PM, joes wrote:

Am Mon, 29 Jul 2024 11:32:00 -0500 schrieb olcott:

On 7/28/2024 3:40 AM, Mikko wrote:

On 2024-07-27 14:21:50 +0000, olcott said:

On 7/27/2024 2:46 AM, Mikko wrote:

On 2024-07-26 16:28:43 +0000, olcott said:
>

No decider is ever accountable for the behavior of the computation
that itself is contained within.

That claim is fully unjustified. How do you even define "accountable"

in the context of computations, automata, and deciders?

 

Halt deciders report the halt status on the basis of the behavior that a
finite string input specifies.

Which is constructed to be the same as the surrounding computation.
 

Did you think that halt deciders report the halt status on some other
basis?

No, what do you think the basis was?
 

Halt deciders are not allowed to report on the behavior of the actual
computation that they themselves are contained within. They are only
allowed to compute the mapping from input finite strings.

What if the input is the same as the containing computation?
 

It always is except in the case where the decider
is reporting on the TM description that itself is
contained within.
When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
(a) Ĥ copies its input ⟨Ĥ⟩
(b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
(c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
(d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩
(e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
(f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
(g) goto (d) with one more level of simulation
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer