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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Computable Functions --- finite string transformation rules
Date: Thu, 24 Apr 2025 23:00:59 -0400
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On 4/24/2025 10:50 PM, olcott wrote:
> On 4/24/2025 6:07 PM, Richard Damon wrote:
>> On 4/24/25 3:41 PM, olcott wrote:
>>> On 4/24/2025 2:12 PM, Fred. Zwarts wrote:
>>>> Op 24.apr.2025 om 19:13 schreef olcott:
>>>>>
>>>>> HHH correctly determines through mathematical induction that
>>>>> DD emulated by HHH (according to the finite string transformations
>>>>> specified by the x86 language) cannot possibly reach its final
>>>>> halt state in an infinite number of steps.
>>>
>>>> No, HHH has a bug which makes that it fails to see that there is 
>>>> only a finite recursion, 
>>>
>>> *You are technically incompetent on this point*
>>> When the finite string transformation rules of the
>>> x86 language are applied to the input to HHH(DD)
>>> THIS DD CANNOT POSSIBLY REACH ITS FINAL HALT STATE
>>> not even after an infinite number of emulated steps.
>>
> 
> 
>> When the defined finite string trasnsformation rules, thos of the x86 
>> language, are applied to this input, completed with the definitions 
>> from Halt7.c as stipulated, we see that DD calls HHH(DD), that it will 
>> spend some time emulating DDm then it will
> 
> Correctly determine that DD emulated by HHH can never possibly
> reach its final halt state even after an infinite number of
> steps are emulated.

Category error.  The fixed code of algorithm HHH, which is part of the 
input as you agreed, emulates for a fixed number of steps.  Therefore 
there is no infinite number of steps emulated by algorithm HHH.

However, UTM(DD) emulates the same input which includes HHH as part if 
it for a finite number of steps and reaches a final state.  The 
instructions emulated by UTM are exactly the same as those emulated by 
HHH up to the point that it aborts, showing that the fixed code of HHH 
is incorrect in showing non-halting.