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On 7/26/2024 3:45 AM, Mikko wrote:That you can say all sorts stupid things does not mean that it be aOn 2024-07-24 13:33:55 +0000, olcott said:We can call everything "late for dinner" with a unique integer
On 7/24/2024 3:57 AM, Mikko wrote:However, Peter Linz does not call taht same thing a difference.On 2024-07-23 13:31:35 +0000, olcott said:The same thing happens at the Peter Linz Turing Machine level
On 7/23/2024 1:32 AM, 0 wrote:That DDD calls HHH and DDD does not call HHH1 is not a differenceOn 2024-07-22 13:46:21 +0000, olcott said:In this case we have two x86utm machines that are identical
On 7/22/2024 2:57 AM, Mikko wrote:The definition of a Turing machine does not say that a Turing machineOn 2024-07-21 13:34:40 +0000, olcott said:Turing machines never take actual Turing machines as inputs.
On 7/21/2024 4:34 AM, Mikko wrote:No, we don't. There is no such prohibition.On 2024-07-20 13:11:03 +0000, olcott said:(b) We know that a decider is not allowed to report on the behavior
On 7/20/2024 3:21 AM, Mikko wrote:You are the lying one.On 2024-07-19 14:08:24 +0000, olcott said:*Because this is true I don't understand how you are not simply lying*
When we use your incorrect reasoning we would concludeYou and your HHH can reason or at least conclude correctly about
that Infinite_Loop() is not an infinite loop because it
only repeats until aborted and is aborted.
Infinite_Loop but not about DDD. Possibly because it prefers to
say "no", which is correct about Infinte_loop but not about DDD.
int main
{
DDD();
}
Calls HHH(DDD) that must abort the emulation of its input
or {HHH, emulated DDD and executed DDD} never stop running.
If HHH(DDD) abrots its simulation and returns true it is correct as a
halt decider for DDD really halts.
computation that itself is contained within.
They only take finite strings as inputs and an actual executing
Turing machine is not itself a finite string.
is not a finite string. It is an abstract mathematical object without
a specification of its exact nature. It could be a set or a finite
string. Its exact nature is not relevant to the theory of computation,
which only cares about certain properties of Turing machines.
Therefore It is not allowed to report on its own behavior.Anyway, that does not follow. The theory of Turing machines does not
prohibit anything.
Another different TM can take the TM description of thisIf a Turing machine can take a description of a TM as its input
machine and thus accurately report on its actual behavior.
or as a part of its input it can also take its own description.
Every Turing machine can be given its own description as input
but a Turing machine may interprete it as something else.
except that DDD calls HHH and DDD does not call HHH1.
between two unnamed turing machines.
I will provide that more difficult example if and only if you
prove that you understand this one.
index and the properties that I assert exist still exist.
When Ĥ is applied to ⟨Ĥ⟩That does not specify a time or a situation.
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
(a) Ĥ copies its input ⟨Ĥ⟩Its not really an invocation. Ĥ imitates H with ⟨Ĥ⟩ ⟨Ĥ⟩.
(b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
(c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩Imitating H, Ĥ simulates ⟨Ĥ⟩ ⟨Ĥ⟩.
(d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩Ĥ, as a part of the simulation of what its input specifecs, simulates
(e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩Again, this is not really an invocation. Imitating H, Ĥ simulates
(f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩Detection that the simulated simulation is identical to the simulating
(g) goto (d) with one more level of simulation
Two complete simulations show a pair of identical TMD's are
simulating a pair of identical inputs. We can see this thus
proving recursive simulation.
When embedded_H is accountable for the behavior of itsEmbedded_H is not accountable for anything. It just is there and does
input and not accountable for the behavior of the
computation that it is contained within then embedded_H
is necessarily correct to transition to its own Ĥ.qn state.
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