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On 5/30/2025 3:45 AM, Mikko wrote:Nope. Where does it say that?On 2025-05-29 18:10:39 +0000, olcott said:That is the same as saying a function with infinite
>On 5/29/2025 12:34 PM, Mr Flibble wrote:>>>
🧠 Simulation vs. Execution in the Halting Problem
>
In the classical framework of computation theory (Turing machines),
simulation is not equivalent to execution, though they can approximate one
another.
To the best of my knowledge a simulated input
always has the exact same behavior as the directly
executed input unless this simulated input calls
its own simulator.
The simulation of the behaviour should be equivalent to the real
behaviour.
recursion must have the same behavior as a function
without infinite recursion.
No it doesn't, as we can only be talking about programs, and programs don't know who "their simulator" is, only what simulator they were built to use.Whether it actually is depends on the quality of theA function that calls its own simulator specifies different
simulator. There is no exception for the case when the simulator
is called. If the behaviour in the simulation is different from
a real execution then the simulation is wrong.
>
behavior than a function that does not call its own simulator.
What "Issue"? Your problme is you don't understand what you are taling about.One of the advantages of Turing machines is that there is no possibilityThe same issue occurs in the Linz proof, it is merely more
to call anything so the effect of calling the simulator need not be
considered.
>
difficult to see. The correctly simulated ⟨Ĥ⟩ ⟨Ĥ⟩ cannot
possibly reach its own simulated final halt state ⟨Ĥ.qn⟩
When Ĥ is applied to ⟨Ĥ⟩Why did the copy of H change to being called "embedded_H"?
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
(a) Ĥ copies its input ⟨Ĥ⟩Which then gets stop when the embedded_H invoked at the first invocation of (b) doing step (c) decides to abort its emulation.
(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
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