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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: My reviewers think that halt deciders must report on the behavior
 of their caller
Date: Thu, 10 Jul 2025 09:04:28 -0500
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On 7/10/2025 5:12 AM, joes wrote:
> Am Wed, 09 Jul 2025 11:06:03 -0500 schrieb olcott:
>> On 7/9/2025 10:42 AM, joes wrote:
>>> Am Wed, 09 Jul 2025 09:06:42 -0500 schrieb olcott:
>>>> On 7/9/2025 8:37 AM, joes wrote:
>>>>> Am Wed, 09 Jul 2025 08:02:16 -0500 schrieb olcott:
>>>>>> On 7/9/2025 3:58 AM, Fred. Zwarts wrote:
> 
>>>>>> All Turing machine deciders only compute the mapping from their
>>>>>> actual inputs. This entails that they never compute any mapping from
>>>>>> non-inputs.
>>>>> It matters more what they map it to, i.e. which mapping they compute.
>>>>> HHH does not compute the halting function.
>>>> It is a matter of verified fact that HHH does correctly determine that
>>>> DDD correctly emulated by HHH cannot possibly reach its own emulated
>>>> final halt state.
>>> Yes. That is not the halting function.
>> Yes it is the halting function.
>> The actual question posed to HHH is:
>> Does your input specify behavior that cannot reach its own final halt
>> state?

> Yes, that is not the mathematical function that pairs encodings of
> programs with their halting state.
> 

It *is* what Turing machine deciders do.
They compute the mapping *FROM THEIR INPUTS*.
based on the behavior that their actual input
actually specifies.

>>> I have another program here that (tautologically) determines that it
>>> cannot simulate ANY code (according to x86 semantics) to a halting
>>> state - by simulating zero steps :-) That tells me nothing about
>>> whether the input halts when executed.
>> That changes the words of the question thus becomes the strawman error.

> No, it answers the same question as HHH: does the simulation halt?
> 

We know that the test program HHH halts.
The program under test: input to HHH(DDD)
cannot possibly reach its own final halt state

>>> How can your beloved Aprove even say anything about its inputs?
> Since programs are not in its domain...
> 

In every case besides pathological self-reference
the correct simulation of an input has the exact
same behavior as the directly executed machine.

The official "received view" behavior of an input
with pathological self-reference is:
*We have no idea what its behavior is and we give up*

>>>>> How could HHH abort and not halt?
>>>> None of the code in HHH can possibly help DDD correctly emulated by
>>>> HHH to reach its own emulated final halt state.
>>> The abort could, if you hadn't botched it with static variables.

>> DDD emulated by HHH according to the semantics of the x86 language
>> continues to emulate the first four instructions of DDD in recursive
>> emulation until HHH aborts its emulation immediately killing every DDD
>> before any of them reach their own "ret" instruction.

> Or before they reach the abort.
> 

The outermost HHH sees that its abort criteria has
been met one whole execution trace sooner then the
next one, thus is the only abort code that can be
reached at that point in the execution trace.

Unless this outermost directly executed HHH aborts
its simulation then none of them ever abort because
every instance of HHH has the exact same machine code.

>> I keep asking for your credentials because you seem to not have enough
>> technical knowledge about ordinary programming.

> Doesn't sound like a degree would convince you.
> 

How many years of professional programming do you have?
I have 20 just in C++. I began my career in 1984.

>>>> The behavior that the input to HHH(DDD) actually specifies is the only
>>>> behavior that any decider can possibly report on.
>>>> That anyone believes that HHH is required to report on the behavior of
>>>> a non-input merely proves a lack of sufficient understanding of how
>>>> Turing machine deciders work.

>>> Yes, what a processor does - turning code into behaviour - is clearly
>>> uncomputable.

> I'll take that as agreement.
> 

No Turing machine ever takes any directly executed
Turing machine as input. Thus no TM halt decider ever
reports on the behavior of any directly executed machine.

TM deciders report on the behavior that their finite
string input specifies. Except in the case of pathological
self-reference this is the same behavior as the directly
executed machine.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer