Re: DDD correctly emulated by HHH is Correctly rejected as non-halting V2 ---woefully mistaken rebuttal

On 26/07/2024 01:53, olcott wrote:

On 7/25/2024 4:03 PM, Mike Terry wrote:

On 25/07/2024 14:56, olcott wrote:

On 7/24/2024 10:29 PM, Mike Terry wrote:

On 23/07/2024 14:31, olcott wrote:

On 7/23/2024 1:32 AM, 0 wrote:

On 2024-07-22 13:46:21 +0000, olcott said:
>

On 7/22/2024 2:57 AM, Mikko wrote:

On 2024-07-21 13:34:40 +0000, olcott said:
>

On 7/21/2024 4:34 AM, Mikko wrote:

On 2024-07-20 13:11:03 +0000, olcott said:
>

On 7/20/2024 3:21 AM, Mikko wrote:

On 2024-07-19 14:08:24 +0000, olcott said:
>

When we use your incorrect reasoning we would conclude
that Infinite_Loop() is not an infinite loop because it
only repeats until aborted and is aborted.

>
You and your HHH can reason or at least conclude correctly about
Infinite_Loop but not about DDD. Possibly because it prefers to
say "no", which is correct about Infinte_loop but not about DDD.
>

>
*Because this is true I don't understand how you are not simply lying*
int main
{
   DDD();
}
>
Calls HHH(DDD) that must abort the emulation of its input
or {HHH, emulated DDD and executed DDD} never stop running.

>
You are the lying one.
>
If HHH(DDD) abrots its simulation and returns true it is correct as a
halt decider for DDD really halts.
>

>
(b) We know that a decider is not allowed to report on the behavior
computation that itself is contained within.

>
No, we don't. There is no such prohibition.
>

>
Turing machines never take actual Turing machines as inputs.
They only take finite strings as inputs and an actual executing
Turing machine is not itself a finite string.

>
The definition of a Turing machine does not say that a Turing machine
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 this
machine and thus accurately report on its actual behavior.

>
If a Turing machine can take a description of a TM as its input
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.
>

In this case we have two x86utm machines that are identical
except that DDD calls HHH and DDD does not call HHH1.
>
It is empirically proven that this changes their behavior
and the behavior of DDD.
>

>
You say a lot about things that are "empirically proven" and without exception they are never "proven" at all.
>

>
It is empirically proven according to the semantics of the
x86 machine code of DDD that DDD correctly emulated by HHH
has different behavior than DDD correctly emulated by HHH1.

>
Perhaps your actual code does behave differently!
>

  OK great, we are making headway.
 

The questions are:
a)  are HHH and HHH1 "identical copies", in the TM machine sense of incorporating
     the algorithm of one TM inside another TM?  (As Linz incorporates H
     inside H^, meaning that the behaviours of H and embedded_H MUST be identical for any
     input.)
     [You claim HHH and HHH1 /are/ proper copies, and yet give different results for
     input (D), which is impossible.]

 They are identical in the that have identical x86 machine
code except for the x86 quirk that function calls are to
a relative rather than absolute address. So when HHH calls
the same function that HHH1 calls the machine code is not
the same.  The only other case where the machine code of
HHH1 and HHH is not identical is the way for slave instances
of HHH to pass its execution trace up to the master.

The relative addressing is to be expected as a difference, and is fine provided the actual target is the same. [Which it seems to be...]
The whole thing with the slave instances might well be where the bug lies!  That would be slightly funny, as I pointed out that problem on some completely unrelated post, and this could be a follow-on issue where it has caused observable misbehavior in the code.  (Needs a bit more investigation...)

 Although it seems that I have been correct all along about the
idea that slave instances can pass their execution trace up to
the master without breaking computability this is not the way
it has been actually encoded.
 Message-ID: <rLmcnQQ3-N_tvH_4nZ2dnZfqnPGdnZ2d@brightview.co.uk>
On 3/1/2024 12:41 PM, Mike Terry wrote:
 >
 > Obviously a simulator has access to the internal state
 > (tape contents etc.) of the simulated machine. No problem there.
 

b)  If the two behaviours HHH/HHH1 are indeed different, WHAT precisely is the coding
     difference that accounts for that different behaviour?  (Like, with your H/H1 the
     difference was that H used H's address as part of its algorithm, while H1 used H1's
     address.)
>

 *I have said this about 500 times in the last three years*
DDD calls HHH(DDD) in recursive simulation and does
not call HHH1(DDD) in recursive simulation.

You may have said it 500 times, but it doesn't answer my question!
Look, here is a rough sketch of the two traces side by side just done by hand:
[VIEW WITH FIXED FONT!!]
   HHH1 (DDD)                          HHH (DDD)
   -----------------------------------------------------------------
1 main ()                             main ()
2   HHH1 (DDD)                          HHH (DDD)
4     Simulate (DDD)                      Simulate (DDD)
5     | DDD()                             | DDD()
6     |   HHH (DDD)                       |   HHH (DDD)
7     |     Simulate (DDD)                |     Simulate (DDD)
8     |     | DDD()                       |       DDD()
9     |     |   HHH (DDD)                 |         HHH (DDD)
10    |     |     Simulate (DDD)          Abort
11    |     |       DDD()                 ret 0
12    |     |         HHH (DDD)         ret 0
13    |     Abort
14    |     ret 0
15    |   ret
16    ret 1
17  ret 0
So HHH/HHH1 behaviour is different, but shouldn't be if HHH1 is a correct copy of HHH.
Your explanation makes NO SENSE AT ALL.  It's just one of those things you repeat 500 times, and nobody bothers to call you out.
You say DDD calls HHH(DDD) in recursive simulation and does not call HHH1 in recursive simulation.
Well that's correct [lines 6,9,12] - but it's irrelevant, because IT'S THE SAME ON BOTH SIDES ABOVE.   Both HHH/HHH1 simulate DDD [line 4] and BOTH of those simulations call HHH in recursive simulation, so BOTH SIDES MUST HAVE THE SAME BEHAVIOUR.
If HHH/HHH1 were just arbitrary emulators, we'd be thinking one of them might abort earlier in the computation than the other, so left/right behaviours above would just match up until the first side aborts.  That is exactly what we see above in my trace comparison.
BUT HHH/HHH1 have identical code and you've said that HHH/HHH1 have no "coding knowledge" of whether they are simulating themselves or something else, e.g. in their abort logic.  So the left/right behaviour should match /all the way down/ since if one side aborts the other side will do so at the same time.  [IF your code copy has been done properly.]
OK, so now for the obvious question!  :)
In the diagram above HHH aborts at line 10.  But HHH1 which has seen exactly the same trace entries [including the two calls to H at lines 6,9] and has the same abort logic [without knowledge of whether it is simulating itself or something else etc.] somehow *decides NOT to abort*.  *WHAT CODE IN HHH/HHH1 IS RESPONSIBLE FOR THAT DIFFERENCE?*

 

>
_DDD()
[00002177] 55         push ebp
[00002178] 8bec       mov ebp,esp
[0000217a] 6877210000 push 00002177
[0000217f] e853f4ffff call 000015d7
[00002184] 83c404     add esp,+04
[00002187] 5d         pop ebp
[00002188] c3         ret
Size in bytes:(0018) [00002188]
>
_main()
[00002197] 55         push ebp
[00002198] 8bec       mov ebp,esp
[0000219a] 6877210000 push 00002177
[0000219f] e863f3ffff call 00001507
[000021a4] 83c404     add esp,+04
[000021a7] 33c0       xor eax,eax
[000021a9] 5d         pop ebp
[000021aa] c3         ret
Size in bytes:(0020) [000021aa]
>
  machine   stack     stack     machine    assembly
  address   address   data      code       language
  ========  ========  ========  =========  =============
[00002197][001037fb][00000000] 55         push ebp
[00002198][001037fb][00000000] 8bec       mov ebp,esp
[0000219a][001037f7][00002177] 6877210000 push 00002177 ; push DDD
[0000219f][001037f3][000021a4] e863f3ffff call 00001507 ; call HHH1
New slave_stack at:10389f
>
Begin Local Halt Decider Simulation   Execution Trace Stored at:1138a7
[00002177][00113897][0011389b] 55         push ebp
[00002178][00113897][0011389b] 8bec       mov ebp,esp
[0000217a][00113893][00002177] 6877210000 push 00002177 ; push DDD
[0000217f][0011388f][00002184] e853f4ffff call 000015d7 ; call HHH
New slave_stack at:14e2c7
>
Begin Local Halt Decider Simulation   Execution Trace Stored at:15e2cf
[00002177][0015e2bf][0015e2c3] 55         push ebp
[00002178][0015e2bf][0015e2c3] 8bec       mov ebp,esp
[0000217a][0015e2bb][00002177] 6877210000 push 00002177 ; push DDD
[0000217f][0015e2b7][00002184] e853f4ffff call 000015d7 ; call HHH
New slave_stack at:198cef
[00002177][001a8ce7][001a8ceb] 55         push ebp
[00002178][001a8ce7][001a8ceb] 8bec       mov ebp,esp
[0000217a][001a8ce3][00002177] 6877210000 push 00002177 ; push DDD
[0000217f][001a8cdf][00002184] e853f4ffff call 000015d7 ; call HHH
Local Halt Decider: Infinite Recursion Detected Simulation Stopped
>
[00002184][00113897][0011389b] 83c404     add esp,+04
[00002187][0011389b][000015bc] 5d         pop ebp
[00002188][0011389f][0003a980] c3         ret
[000021a4][001037fb][00000000] 83c404     add esp,+04
[000021a7][001037fb][00000000] 33c0       xor eax,eax
[000021a9][001037ff][00000018] 5d         pop ebp
[000021aa][00103803][00000000] c3         ret
Number of Instructions Executed(352831) == 5266 Pages
>

>
that seems to be a (partial) trace of HHH1(D).  It's not clear exactly what's happening - for example, who produces the message "Local Halt Decider: Infinite Recursion Detected Simulation Stopped"?  It might be outer HHH1 or one of the inner HHH's.  And what result did HHH1 report?
>

 It is supposed to be the outer most (thus directly executed) HHH.

HHH is not directly executed in this trace - HHH1 is.  But the message is not from HHH1, it's from the 1st level of emulation HHH is being emulated.  (line 7 in my trace above)  That is not easy to deduce from your trace log - you should include an "emulation level" column to make this clear, like I suggested a couple of years ago!

 

And more to the point what did HHH(D) do, and what is the difference?
>

 *I have said this about 500 times in the last three years*
DDD calls HHH(DDD) in recursive simulation and does
not call HHH1(DDD) in recursive simulation.
 When a function unconditionally calls itself this is infinite
recursion.
 When a function unconditionally calls its own simulator this is
infinite recursive simulation. HHH sees this as infinite recursion
because HHH does not know that DDD is calling itself.

First off, it need not be /infinite/ recursive simulation, because you have neglected the conditional logic in H which determines whether or not to abort a simulation.  It makes no difference to termination analysis if the conditionals are in DDD or HHH - the latter is a direct extension of the former.  In your terminology we might say it is "part of the finite string representing the DDD machine".
Secondly, if HHH sees what it thinks is "infinite recursion", then the same pattern occured when HHH1 was simulating, and so HHH1 should have seen the pattern and aborted at the same point.  *Why didn't it do that?*
LOL, given your earlier remark above about your faulty implentation of "slave" emulators passing stuff to the "master" emulator, and together with my [super-clear!] trace comparison, I've worked out what's happening!
I'll let you think it through first though.
Mike.