Re: Halting Problem: What Constitutes Pathological Input

On 07/05/2025 04:11, olcott wrote:

On 5/6/2025 9:53 PM, Mike Terry wrote:

On 07/05/2025 00:11, olcott wrote:

On 5/6/2025 5:49 PM, Mike Terry wrote:

On 06/05/2025 21:25, olcott wrote:

On 5/6/2025 2:35 PM, dbush wrote:

On 5/6/2025 2:47 PM, olcott wrote:

On 5/6/2025 7:14 AM, dbush wrote:

On 5/6/2025 1:54 AM, olcott wrote:

On 5/6/2025 12:49 AM, Richard Heathfield wrote:

On 06/05/2025 00:29, olcott wrote:
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<snip>
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It is the problem incorrect specification that creates
the contradiction.

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Not at all. The contradiction arises from the fact that it is not possible to construct a universal decider.
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Everyone here insists that functions computed
by models of computation can ignore inputs and
base their output on something else.

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I don't think anyone's saying that.
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Maybe you don't read so well.
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What are the exact steps for DD to be emulated by HHH
according to the semantics of the x86 language?
*Only an execution trace will do*

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The exact same steps for DD to be emulated by UTM.
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_DD()
[00002133] 55         push ebp      ; housekeeping
[00002134] 8bec       mov ebp,esp   ; housekeeping
[00002136] 51         push ecx      ; make space for local
[00002137] 6833210000 push 00002133 ; push DD
[0000213c] e882f4ffff call 000015c3 ; call HHH(DD)
[00002141] 83c404     add esp,+04
[00002144] 8945fc     mov [ebp-04],eax
[00002147] 837dfc00   cmp dword [ebp-04],+00
[0000214b] 7402       jz 0000214f
[0000214d] ebfe       jmp 0000214d
[0000214f] 8b45fc     mov eax,[ebp-04]
[00002152] 8be5       mov esp,ebp
[00002154] 5d         pop ebp
[00002155] c3         ret
Size in bytes:(0035) [00002155]
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Machine address by machine address specifics
that you know that you cannot provide because
you know that you are wrong.
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HHH and UTM emulate DD exactly the same up until the point that HHH aborts,

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When you trace through the actual steps you
will see that this is counter-factual.

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No, it is exactly right.  Remember, I posted a comparison of the two traces side by side some time ago, and they were indeed IDENTICAL line for line up to the point where HHH decided to discontinue simulating.

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That is counter-factual.

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Dude!  :/  I posted the comparison and the traces were the same up to the point where HHH discontinued the simulation.  How can it be "counter-factual"?
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 HHH1(DD) the call from DD to HHH(DD) returns.
HHH(DD) the call from DD to HHH(DD) cannot possibly return.
 A call that returns and a call that cannot possibly
return *are not exactly the same thing*

You need to read what posters actually say.  I said the traces were the same up to the point where HHH stops simulating.  I didn't say anything about calls that return or do not return "being the same thing" and none of what you relates to whether what I said was correct.
Look, if you insist the traces are not the same up to the point where HHH stops simulating, show the two traces and we'll just look and see!  Simples.
At this point, no need to be too formal, just a high level trace, e.g. referencing C code rather than instruction addresses...

 

HHH1(DD) the call from DD to HHH(DD) returns.
HHH(DD) the call from DD to HHH(DD) cannot possibly return.
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<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
     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
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     *input D* refers to the actual HHH/DD pair

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..which is not to be changed during hypothetical modifications to H

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     *would never stop running unless aborted*
      refers to the hypothetical HHH/DD pair where
      HHH and DDD are exactly the same except that
      this hypothetical HHH does not abort the
      simulation of its input.

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No, that doesn't work in your x86utm because you mix up code (HHH) and data (DD, which directly calls HHH).  DD must be "exactly the same" / including all its subroutines/,

 Not at all. Professor Sipser agreed that the actual
HHH/DD must base its decision on the hypothetical
HHH/DD that never aborts its simulation.

Nonsense.  He is taking it as read that the input is not changed.  What he agreed was that the actual HHH can base its decision on the hypothetical HHH that never aborts its simulation, running against *identical input* DD.  Identical means has identical behaviour to original DD, in particular it calls original HHH, not some modified HHH or UTM.
Of course, Sipser would not understand how you have mangled the design of your utmx86 environment. He would naturally take it that you were correctly implementing basic features of the TM halting problem, like the input data being totally distinct from the TM state table.  So it would simply never occur to him that in your world, changing the code of HHH would have any effect on the data input DD, which explains why he does not explicitly mention that.

 *would never stop running unless aborted*
*would never stop running unless aborted*
*would never stop running unless aborted*

yawn

 

but DD calls HHH so HHH must be exactly the same, otherwise the input has been changed which is NOT ALLOWED.
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 Intuitively it would seem that way until you examine
every single detail 100% completely.
 

To make this work you have to create a /new/ "HHH that does not abort the simulation".

 Professor Sipser already agreed that the actual HHH/DD
must base its decision on the hypothetical HHH/DD
that never aborts.

You are quite incapable of understanding what Sipser was agreeing to.  More generally you have a problem understanding what other people believe and what they are communicating to you.  I've suggested you have some neural wiring issue, and for sure this would be tied in to that somehow.
Regardless of that, you are trying to use Sipser's quote as an appeal to authority, which you understand is a fallacy but think its ok to do it anyway.  [Even though you are quick to accuse other people of doing that when it suits you.]
Just stop mentioning Sipser's quote altogether!  It is not helping your case in any shape or form.

 

E.g. clone HHH to HHH_hypothetical then take out the abort logic from HHH_hypothetical.  From main() call HHH_hypothetical(DD).  That way DD is unchanged as required.
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The trace by UTM continued further, with DD returning some time later.
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The above HHH1(DD) is this UTM.

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HHH1 will serve in this case, since it happens to not abort due to your coding errors.

 It does not happen to not abort due to coding
errors. That is a reckless disregard for the truth.
The code has specified exactly why it need not
abort for several years now.

No, it's due to coding errors.  You intended HHH1 to be a clone of HHH, with the same algorithm as HHH, but at a different address.  You just screwed it up due to your inappropriate use of global variables.  If you had coded things correctly HHH(DD) and HHH1(DD) would both have (incorrectly) decided halts.  I explained the gory details of all this to you months/years ago.

 

 It would be cleaner to make a function UTM() which just has the DebugStep loop and no abort logic.
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 Professor Sipser already agreed that the actual HHH/DD
must base its decision on the hypothetical HHH/DD
that never aborts, AKA your UTM.

Sipser would be ok with my UTM, simulating THE ORIGINAL DD, which calls THE ORIGINAL HHH.
In other words UTM(DD), where UTM is a /separate function/ from HHH, and has been called from main() instead of HHH, where meanwhile HHH has not been changed.
If you edit the actual HHH in your halt7.c and recompile etc., you are clearly changing the input, which Sipser would never agree to.
[/NOBODY/ would agree to that, as it's just bonkers!]

 

So... are you saying that HHH has seen enough of the simulation to correctly determined that HHH1(DD) never returns?  That would be bizarre, since you know HHH1(DD) /does/ return.
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Yes or no?  Do you understand the question?

 Functions computed by models of computation must
apply the steps of an algorithm *to the input*
to derive the outputs.

duffer-speak.  Of course TMs etc. apply their algorithm "to the input".  That is all that TMs can do, so saying they have to do it shows a basic confusion in your understanding.  I don't care to get to the bottom of that, so I'll just ignore it.

 HHH has seen enough of the execution trace of DD
to know that
 *simulated D would never stop running unless aborted*
This refers to the hypothetical HHH/DD pair such that
HHH never aborts.

...and input D is unchanged, so still calls original H.
But then your D [= DD] /WILL/ stop running if not aborted.  UTM(DD) confirms this claim, and it /sees/ DD return, and above you seem to be admitting that Sipser's criterion is that UTM(DD) will never stop running.  So his criterion does not apply to your HHH/DD.
The long and short of it seems to be that you want to:
a)  edit HHH to not abort
b)  keep DD calling HHH which now does not abort  [thus changing the input being considered]
c)  observe that this new DD never halts.
(c) is true, and everyone understands this, but
*(c) is not the crierion on which HHH must decide*.
HHH must decide whether "DD() halts".  Equivalently, whether independently executed DD() halts, which is the same as whether UTM(DD) halts [where DD still calls original HHH which is distinct from UTM], which is what Sipser is saying in his quote.
As long as you are thinking (a),(b),(c) there is no point posting here, since everybody knows that is Wrong Wrong Wrong, and nobody understanding HP is ever going to change their mind on that, so you are just wasting everybody's time, including your own!  It would be best to spend your time studying posters objections on why that is wrong, and only post here again when you've understood your error.
Regards,
Mike.