Re: Linz's proofs and other undecidable decision problems [LP as basis] [Mike Terry]

On 5/12/24 10:18 AM, olcott wrote:

On 5/12/2024 2:47 AM, Mikko wrote:

On 2024-05-11 16:06:29 +0000, olcott said:
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On 5/11/2024 3:00 AM, Mikko wrote:

On 2024-05-10 18:16:37 +0000, olcott said:
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On 3/1/2024 12:41 PM, Mike Terry wrote:

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Obviously a simulator has access to the internal state (tape contents etc.) of the simulated machine.  No problem there.
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What isn't allowed is the simulated machine altering its own behaviour by accessing data outside of its own state.  (I.e. accessing data from its parent simulators state.)
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While an "active-simulator" [my own term] is at liberty to combine
straight simulation with add-on "enhancements" that extend the
functionality of the simulated machine, in doing so it would no
longer be a simulator in the sense you need it to be.  So you
mustn't do this!

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In principle an incorrect simulation is permissible. However, to prove
that the result inferred from an incorrect simulation is correct may
be impossible.
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Within the conventional terms-of-the-art of {termination analyzer}
and {simulator} an incorrect simulation is forbidden.

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The conventional meaning of "termination analyzer" does not prohibit
incorrect simulation.

 If it does not correctly determine termination then it is not
a termination analyzer.

And thus, since D(D) does terminate, your H is wrong.

 

 Whether an incorrect simulation can be called
"simulation" is a matter of opinion.

 One can call a {dead cat} a fifteen story office building. One
cannot correctly call a {dead cat} a fifteen story office building.

And you can not correctly call a halting program as non-halting.
Since D(D) Halts, H(D,D) saying it doesn't is just wrong.
ALL your logic eventually goes back to assuming an incorrect statement, Like that H does correctly simulate its input, or that H is both a single machine and also an infinite set of machines, or that H can analyze a D that calls some other H then the one that the one it is looking at works on.
Also, you have effectively admitted to just being a liar, as the conventional definition as a term-of-art for either a Halt Decider, or a Terminataion Analyzer, is that their input is a description of a PROGRAM, a SPECIFIC program, but your H doesn't take in a specific program, but a "template" that changes the input as we apply different deciders to it.

 Ignoring the input and simulating zero steps cannot be correctly
called a simulation. Correctly simulating the first step of an
input is a correct simulation by definition. It is not a correct
and complete simulation when the input has more than one step.
 

You miss that it is just as valid as simulating N steps, and then use invalid logic t get the wrong answer. You keep on trying to change you definitions to hide your various errors.
If YOUR H is allowed to ignore the actual behavior of the input given to it (which calls itself, and thus assume that the H that this D calls doesn't return, when it is defined as THIS H, which does return, then it is just as valid to totally ignore the input.

In any case, when a methind that
uses an incorrect simulation is described the incorrectness of the
simulation, whther calles "simulation" or otherwise, must be mentioned
and its role be explained.
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