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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory,sci.logic
Subject: Re: Why does Olcott care about simulation, anyway? --- Ben's Review
Date: Mon, 3 Jun 2024 22:09:59 +0200
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Op 03.jun.2024 om 14:20 schreef olcott:
> On 6/3/2024 4:42 AM, Ben Bacarisse wrote:
>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>>
>>> PO's D(D) halts, as illustrated in various traces that have been 
>>> posted here.
>>> PO's H(D,D) returns 0 : [NOT halting] also as illustrated in various 
>>> traces.
>>> i.e. exactly as the Linz proof claims.  PO has acknowledged both these
>>> results.  Same for the HH/DD variants.
>>>
>>> You might imagine that's the end of the matter - PO failed.  :)
>>>
>>> That's right, but PO just carries on anyway!
>>
>> He has quite explicitly stated that false (0) is the correct result for
>> H(D,D) "even though D(D) halts".  I am mystified why anyone continues to
>> discuss the matter until he equally explicitly repudiates that claim.
>>
> 
> Deciders only compute the mapping *from their inputs* to their own
> accept or reject state. The correct emulation of the machine code input
> to H(DD,DD) requires DD emulated by HH to emulate each x86 instruction
> of the x86 machine code of DD correctly and in the correct order.
> 
> *The input to HH(DD,DD) specifies non-halting behavior*
> 
> The only way to cause DD emulated by HH to have the same behavior as
> the directly executed (non input) DD(DD) is to emulate the instructions
> specified by the machine code of DD incorrectly or in the incorrect
> order. *This is not the behavior that the input to HH(DD,DD) specifies*
> 
> The behavior of the directly executed DD(DD) has different behavior
> than DD correctly emulated by HH. This is because the behavior of DD(DD)
> reaps the benefits of HH having already aborted its simulation.
> 
> No one ever noticed that these two behaviors could ever diverge before
> because everyone rejected the notion of a simulating halt decider out-
> of-hand without review.
> 
> 
> 
> Two PhD computer science professors that I have communicated with
> agree with me that there is something wrong with the halting problem.
> 
> Bill Stoddart. *The Halting Paradox*
> 20 December 2017
> https://arxiv.org/abs/1906.05340
> arXiv:1906.05340 [cs.LO]
> 
> E C R Hehner. *Problems with the Halting Problem*, COMPUTING2011 
> Symposium on 75 years of Turing Machine and Lambda-Calculus, Karlsruhe 
> Germany, invited, 2011 October 20-21; Advances in Computer Science and 
> Engineering v.10 n.1 p.31-60, 2013
> https://www.cs.toronto.edu/~hehner/PHP.pdf
> 
> E C R Hehner. *Objective and Subjective Specifications*
> WST Workshop on Termination, Oxford.  2018 July 18.
> See https://www.cs.toronto.edu/~hehner/OSS.pdf
> 
> 
> 
> *Introduction to the Theory of Computation, by Michael Sipser*
> https://www.amazon.com/Introduction-Theory-Computation-Michael-Sipser/dp/113318779X/
> 
> On 10/13/2022 11:29:23 AM
> MIT Professor Michael Sipser agreed this verbatim paragraph is correct
> (He has neither reviewed nor agreed to anything else in this paper)
> 
> <Professor Sipser agreed>
> If simulating halt decider H correctly simulates its input D until H
> correctly determines that its simulated D would never stop running
> unless aborted then
> 
> H can abort its simulation of D and correctly report that D specifies a
> non-halting sequence of configurations.
> </Professor Sipser agreed>
> 
> 
> 
> *DD correctly simulated by HH would never stop running unless aborted*
> *We can see that the following DD cannot possibly halt when*
> *correctly simulated by every HH that can possibly exist*

It is very clear that if the simulated HH would halt, then DD would 
halt. So your claim comes down to HH not halting when simulating itself.

It also shows that the simulator does not even reach the pathological 
part (lines 04, 05 and 06) of DD, where it contradicts the result of HH. 
Your own claim is that these lines are not processed by the simulator.
The simulator is unable to process anything past the call to itself.

This shows that by introducing a simulation, you introduced another 
non-halting problem. Every function that calls HH, even when it does not 
contradict HH are suddenly non-halting. This non-halting problem is very 
different from the one in the Linz proof.

> 
> typedef int (*ptr)();  // ptr is pointer to int function in C
> 00       int HH(ptr p, ptr i);
> 01       int DD(ptr p)
> 02       {
> 03         int Halt_Status = HH(p, p);
> 04         if (Halt_Status)
> 05           HERE: goto HERE;
> 06         return Halt_Status;
> 07       }
> 
> _DD()
> [00001c22] 55         push ebp
> [00001c23] 8bec       mov ebp,esp
> [00001c25] 51         push ecx
> [00001c26] 8b4508     mov eax,[ebp+08]
> [00001c29] 50         push eax        ; push DD 1c22
> [00001c2a] 8b4d08     mov ecx,[ebp+08]
> [00001c2d] 51         push ecx        ; push DD 1c22
> [00001c2e] e80ff7ffff call 00001342   ; call HH
> [00001c33] 83c408     add esp,+08
> [00001c36] 8945fc     mov [ebp-04],eax
> [00001c39] 837dfc00   cmp dword [ebp-04],+00
> [00001c3d] 7402       jz 00001c41
> [00001c3f] ebfe       jmp 00001c3f
> [00001c41] 8b45fc     mov eax,[ebp-04]
> [00001c44] 8be5       mov esp,ebp
> [00001c46] 5d         pop ebp
> [00001c47] c3         ret
> Size in bytes:(0038) [00001c47]
> 
> 
> 
>>> So really, there's no /need/ to "refute" everything he says - the end
>>> result will be exactly the same as just ignoring him, BUT WITH THE 
>>> LATTER
>>> ONLY NEEDING 0.1% OF THE EFFORT and eliminating 99.9% of the posting
>>> clutter in these newsgroups.  [ok, comp.theory will die pretty 
>>> quickly, but
>>> it is not discussing anything useful, so that's ok for most people... 
>>> (with
>>> some reluctance)]
>>
>> Do we know that?  There's the start of a discussion of quines on
>> comp.lang.c that probably belongs here, but no will dare come here to
>> discuss it because of all the junk.
>>
> 
> You cannot show any mistake in what I said above because all you
> have is bluster and dogma. What I am saying is just not the way
> that you memorized it !
>