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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD specifies recursive emulation to HHH and halting to HHH1
Date: Thu, 27 Mar 2025 14:27:15 -0400
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On 3/27/2025 1:50 PM, olcott wrote:
> On 3/27/2025 2:18 AM, Fred. Zwarts wrote:
>> Op 27.mrt.2025 om 04:09 schreef olcott:
>>> On 3/26/2025 8:22 PM, Richard Damon wrote:
>>>
>>> _DDD()
>>> [00002172] 55         push ebp      ; housekeeping
>>> [00002173] 8bec       mov  ebp,esp  ; housekeeping
>>> [00002175] 6872210000 push 00002172 ; push DDD
>>> [0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
>>> [0000217f] 83c404     add  esp,+04
>>> [00002182] 5d         pop  ebp
>>> [00002183] c3         ret
>>> Size in bytes:(0018) [00002183]
>>>
>>>> Non-Halting is that the machine won't reach its final staste even if 
>>>> an unbounded number of steps are emulated. Since HHH doesn't do 
>>>> that, it isn't showing non-halting.
>>>>
>>>
>>> DDD emulated by any HHH will never reach its final state
>>> in an unbounded number of steps.
>>>
>>> DDD emulated by HHH1 reaches its final state in a finite
>>> number of steps.
>>>
>> It is not very interesting to know whether a simulator reports that it 
>> is unable to reach the end of the simulation of a program that halts 
>> in direct execution.
> 
> That IS NOT what HHH is reporting.
> HHH correctly rejects DDD because DDD correctly
> emulated by HHH cannot possibly reach its own
> final halt state.

In other words, HHH is not a halt decider because it is not computing 
the required mapping:


Given any algorithm (i.e. a fixed immutable sequence of instructions) X 
described as <X> with input Y:

A solution to the halting problem is an algorithm H that computes the 
following mapping:

(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly


> 
>> It is interesting to know:
>> 'Is there an algorithm that can determine for all possible inputs 
>> whether the input specifies a program that (according to the semantics 
>> of the machine language) halts when directly executed?'
> 
> It is the halts while directly executed that is impossible
> for all inputs.

In other words, you *once again* explicitly agree with Linz and others 
that no algorithm behaves as required above.

> A TM can only report on the behavior that the machine code
> of another TM specifies. 

And the machine code of DDD specifies that it halts when executed directly.

> When it specifies a pathological
> relationship then the behavior caused by the pathological
> relationship MUST BE REPORTED.

False.  The behavior that must be reported is what the requirements 
stipulate:


Given any algorithm (i.e. a fixed immutable sequence of instructions) X 
described as <X> with input Y:

A solution to the halting problem is an algorithm H that computes the 
following mapping:

(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly


> 
>> This question seems undecidable for Olcott.
>>
>>
> 
>