Re: How Partial Simulations correctly determine non-halting ---Ben's 10/2022 analysis

On 6/7/24 11:36 PM, olcott wrote:

On 6/7/2024 10:03 PM, Richard Damon wrote:

On 6/7/24 10:43 PM, Mike Terry wrote:

On 07/06/2024 17:34, joes wrote:

Am Fri, 07 Jun 2024 10:40:37 -0500 schrieb olcott:

On 6/7/2024 10:32 AM, joes wrote:

Am Fri, 07 Jun 2024 10:20:09 -0500 schrieb olcott:

On 6/7/2024 10:09 AM, Python wrote:

Le 07/06/2024 à 17:05, olcott a écrit :

On 6/7/2024 9:55 AM, Python wrote:

Le 07/06/2024 à 16:47, olcott a écrit :

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The issue here is that I proved that DD correctly simulated by HH
has different behavior than the directly executed DD(DD) and
everyone's "rebuttal" to this proof is to simply ignore it.

When you actually try to form a rebuttal of the above you will see
that I am correct. So far everyone simply ignores the proof that I
am correct as their only rebuttal.

A {correct simulation} means that each instruction of the above x86
machine language of DD is correctly simulated by HH and simulated in
the correct order.

And to the end. Thus it can't behave differently than direct execution.

You must not be very good at programming if you believe that
Infinite_Recursion must be simulated "to the end"

As I said before, if there is no end the simulation can't end either.

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PO chooses to leave his terminology ambiguous, so we have 1000 post threads perpetuated by little more than verbal misunderstandings.
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All PO's "simulating halt deciders" (SHD) are actually "partial simulating partial halt deciders":
They partially simulate their input computation, while monitoring the simulation state for patterns which *PO* just believes (without proof) indicate non-halting.  When such a pattern is detected, the SHD abandons its simulating activity ["aborts" its simulation], and returns nonhalting.  Also, PO does not claim that his SHDs decide all inputs correctly - or even that they halt for all inputs (which a decider must).  He is really just interested in the H(D,D) case.
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PO has a couple of such rules/patterns, and at least one of them is sound: the "tight loop" pattern.  If an input (P,I) contains a tight loop (like "LOOP: goto LOOP"), and assuming PO has coded the rule correctly, his H/HH will detect the tight loop while simulating the code and correctly return non-halting.  In this scenario we have a non-terminating computation, but PO's /partial/ simulation obviously ends through aborting the target.  THERE'S NOTHING WRONG WITH THAT. If someone wants to claim "that's not valid simulation" then right or wrong it's nothing more than a disagreement over use of terminology, and nothing is achieved by that.
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PO also has at least one /unsound/ rule: his "infinite recursive simulation" rule.  That rule matches computations that in fact halt. Despite PO's colourful language like "...until H 'sees that the simulation will never terminate unless blah blah'" and "...DD 'specifies infinite recursion to HH'" and so on, the truth is simply that his H is applying an unsound rule, which leads to it deciding incorrectly.)
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And all the stuff about "correct simulations of DD by HH never reaching line nn" might be correct if suitably interpreted (as /partial simulations/ not reaching a simulated halt state, rather than the /actual computation/ being examined), but its all logically irrelevent having little to do with actual termination of a given computation.
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What makes the SHD work or not work is the matching of rules (patterns detected in the simulated computation states) that the SHD uses to trigger an abort.  If a /sound/ rule matches, the SHD will decide correctly. If an /unsound/ rule matches it may decide incorrectly (as with PO's H(D,D)), or in other situations it might be correct "by fluke".
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If PO's H used only sound rules, it would not decide input (D,D) incorrectly - but unfortunately neither would it decide correctly - it would never terminate /for that input/.  (I find that kind of neat...)
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Anyone claiming that HH should report on the behavior of the directly
executed DD(DD) is requiring a violation of the above definition of
correct simulation.

But those are the same. How does simulating something change it?

It seems to boil down to you just don't know enough about programming
otherwise it would occur to you that there cannot possibly exist any
correct rebuttal to the following:

Answer the question. Why should the simulation differ from direct
execution?

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[Let's assume code is properly restricted to exclude the complications of "cheating" in PO's x86utm environment through use of mutable static variables and the like.]
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Obviously they wouldn't, except in so far as "partial simulation" differs from "full simulation". I.e. all steps will match precisely, up to the point where the partial simulation is abandoned.
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And in PO's H(D,D) vs D(D) example that is exactly what the traces show:  The simulated and direct traces match exactly, right up to the point where H aborts the simulation.  (The full computation steps of D(D) then proceeding further until D terminates a bit later.)
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Even though I put the two traces side-by-side for PO, he still insists the "behaviour is different".  Well, perhaps he just means that the H simulation was abandonned whereas directly executed D(D) proceeded further and eventually terminated?  If so, then /so what/?  I think his problem here is nothing to do with /simulations/ not reaching whatever line of code, but more the /reason/ that his H aborted - it matched his (unsound) non-halting pattern, and he just really really really really believes that pattern is sound.
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So now he needs to account for two "verified facts":  1)  D(D) computation never halts (/his unsound pattern matched!/)  2) D(D) computation halts when run directly.  That forces him to claim there are two different behaviours [/beyond/ the simple truncation of the aborted trace] for the one computation, and to come up with some Words to justify that position (like "pathological self reference", subjective questions) and then More Words to say that his other Words are "the true meaning of halting" etc. etc.  All nonsense flowing from not being able to accept his rule is just wrong.
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Mike.
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The last time I remember him actually trying to answer, the difference was that the order of who started mattered, because D(D) calling H(D,D) meant that the H(D,D) that was called doesn't get stuck in the loop, but recognizes the loop and gets out, while when H(D,D) simulated D(D) and that first H(D,D) sees that the simulated H(D,D) would just get into a loop, that incorrect decision becomes the actual behavior of that simulated H(D,D).
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So it is always the first H(D,D) that returns, and the second one doesn't, which just proes that is can't be a pure function, or that rule doesn't apply to functions whose simulation has been aborted.
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Of course he also think that aborting th simulation mean that hte machine being simulate had its plug pulled at that point, so it isn't proper to look at the direct execution after that,
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He clearly doesn't seem to understand how these sorts of machines work.

 DD(DD) is just like infinite recursion that gets terminated at
its second recursive call. DD(DD) halts only because HH(DD,DD)
correctly determines that its input DOES NOT HALT.

Except a potentially infinite loop that has code that breaks out of that loop will halt.
Since DD included HH as part of it, if that included part will stop DD from running forever (by keeping that HH from running forever) then DD is not a non-halting program.
The fact that the HH simulating this DD aborts isn't what makes DD non-halting, but the presence of that does mean (since DD is built from HH) that DD has within it the code to stop it from running forever.

 If HH(DD,DD) did not correctly determine that its input
DOES NOT HALT then DD(DD) would never halt.
 

But your problem is that since HH DOES decide to abort its simulation and return 0, that IS what it does, and that makes DD "potential" infinite loop, finite.
Thus, when HH does abort its simulation, that makes DD Halting, and if HH doesn't abort its simulation, it makes both DD and HH non-halting (which makes HH not a decider).
The point you keep on missing is that HH is a specific machine, and has made its decision by its design, and by the way DD is constructed, that affects what DD Does.