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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD specifies recursive emulation to HHH and halting to HHH1
Date: Sat, 29 Mar 2025 22:38:18 -0500
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On 3/29/2025 9:49 PM, dbush wrote:
> On 3/29/2025 10:35 PM, olcott wrote:
>> On 3/29/2025 8:12 PM, Richard Damon wrote:
>>> On 3/29/25 6:44 PM, olcott wrote:
>>>> On 3/29/2025 5:08 PM, dbush wrote:
>>>>> On 3/29/2025 5:46 PM, olcott wrote:
>>>>>> On 3/29/2025 3:14 PM, dbush wrote:
>>>>>>> On 3/29/2025 4:01 PM, olcott wrote:
>>>>>>>> On 3/29/2025 2:26 PM, dbush wrote:
>>>>>>>>> On 3/29/2025 3:22 PM, olcott wrote:
>>>>>>>>>> On 3/29/2025 2:06 PM, dbush wrote:
>>>>>>>>>>> On 3/29/2025 3:03 PM, olcott wrote:
>>>>>>>>>>>> On 3/29/2025 10:23 AM, dbush wrote:
>>>>>>>>>>>>> On 3/29/2025 11:12 AM, olcott wrote:
>>>>>>>>>>>>>> On 3/28/2025 11:00 PM, dbush wrote:
>>>>>>>>>>>>>>> On 3/28/2025 11:45 PM, olcott wrote:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> It defines that it must compute the mapping from
>>>>>>>>>>>>>>>> the direct execution of a Turing Machine
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Which does not require tracing an actual running TM, only 
>>>>>>>>>>>>>>> mapping properties of the TM described. 
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The key fact that you continue to dishonestly ignore
>>>>>>>>>>>>>> is the concrete counter-example that I provided that
>>>>>>>>>>>>>> conclusively proves that the finite string of machine
>>>>>>>>>>>>>> code input is not always a valid proxy for the behavior
>>>>>>>>>>>>>> of the underlying virtual machine.
>>>>>>>>>>>>>
>>>>>>>>>>>>> In other words, you deny the concept of a UTM, which can 
>>>>>>>>>>>>> take a description of any Turing machine and exactly 
>>>>>>>>>>>>> reproduce the behavior of the direct execution.
>>>>>>>>>>>>
>>>>>>>>>>>> I deny that a pathological relationship between a UTM and
>>>>>>>>>>>> its input can be correctly ignored.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> In such a case, the UTM will not halt, and neither will the 
>>>>>>>>>>> input when executed directly.
>>>>>>>>>>
>>>>>>>>>> It is not impossible to adapt a UTM such that it
>>>>>>>>>> correctly simulates a finite number of steps of an
>>>>>>>>>> input.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> 1) then you no longer have a UTM, so statements about a UTM 
>>>>>>>>> don't apply
>>>>>>>>
>>>>>>>> We can know that when this adapted UTM simulates a
>>>>>>>> finite number of steps of its input that this finite
>>>>>>>> number of steps were simulated correctly.
>>>>>>>
>>>>>>> And therefore does not do a correct UTM simulation that matches 
>>>>>>> the behavior of the direct execution as it is incomplete.
>>>>>>>
>>>>>>
>>>>>> It is dishonest to expect non-terminating inputs to complete.
>>>>>
>>>>> An input that halts when executed directly is not non-terminating
>>>>>
>>>>>>
>>>>>>>>
>>>>>>>>> 2) changing the input is not allowed
>>>>>>>>
>>>>>>>> The input is unchanged. There never was any
>>>>>>>> indication that the input was in any way changed.
>>>>>>>>
>>>>>>>
>>>>>>> False, if the starting function calls UTM and UTM changes, you're 
>>>>>>> changing the input.
>>>>>>>
>>>>>>
>>>>>> When UTM1 is a UTM that has been adapted to only simulate
>>>>>> a finite number of steps 
>>>>>
>>>>> And is therefore no longer a UTM that does a correct and complete 
>>>>> simulation
>>>>>
>>>>>> and input D calls UTM1 then the
>>>>>> behavior of D simulated by UTM1 
>>>>>
>>>>>
>>>>> Is not what I asked about.  I asked about the behavior of D when 
>>>>> executed directly.
>>>>>
>>>>
>>>> Off topic for this thread.
>>>> UTM1 D DOES NOT HALT
>>>> UTM2 D HALTS
>>>> D is the same finite string in both cases.
>>>>
>>>
>>> No it isn't, not if it is the definition of a PROGRAM.
>>>
>>
>> _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]
>>
>> The behavior that these machine code bytes specify:
>> 558bec6872210000e853f4ffff83c4045dc3
> 
> As well as the machine code bytes of the function HHH and the machine 
> code bytes of everything that HHH calls down to the OS level, is that of 
> a program that halts when executed directly, which is the required 
> behavior to report on.
> 
> 

The test program must ignore its own behavior when
testing the program-under-test.

The Peter Linz proof explicitly includes the halt
decider embedded within it. The principle is the same.

When Ĥ is applied to ⟨Ĥ⟩ it reaches Ĥ.qn
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

When embedded_H is applied to ⟨Ĥ⟩ ⟨Ĥ⟩ then ⟨Ĥ⟩
does not reach either ⟨Ĥ.qy⟩ or ⟨Ĥ.qn⟩


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