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Subject: Re: How Partial Simulations correctly determine non-halting ---Ben's
 10/2022 analysis
Newsgroups: comp.theory
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From: Mike Terry <news.dead.person.stones@darjeeling.plus.com>
Date: Sat, 8 Jun 2024 03:43:57 +0100
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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 :
> 
>>>>>>>> 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.

PO chooses to leave his terminology ambiguous, so we have 1000 post threads perpetuated by little 
more than verbal misunderstandings.

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.

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.

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.)

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.

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".

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...)

> 
>>>> 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?

[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.]

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.

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.)

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.

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.


Mike.