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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: HHH(DD) --- COMPUTE ACTUAL MAPPING FROM INPUT TO OUTPUT --- Using
 Finite String Transformations
Date: Thu, 24 Apr 2025 22:09:21 +0200
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Op 24.apr.2025 om 21:49 schreef olcott:
> On 4/23/2025 7:31 PM, Mike Terry wrote:
>> On 23/04/2025 16:38, olcott wrote:
>>> On 4/23/2025 10:28 AM, Mike Terry wrote:
>>>> On 23/04/2025 10:02, Fred. Zwarts wrote:
>>>>> Op 22.apr.2025 om 21:50 schreef olcott:
>>>>>> On 4/22/2025 2:30 PM, Fred. Zwarts wrote:
>>>>>>> Op 22.apr.2025 om 21:14 schreef olcott:
>>>>>>>> On 4/22/2025 1:10 PM, Fred. Zwarts wrote:
>>>>>>>>> Op 22.apr.2025 om 18:38 schreef olcott:
>>>>>>>>>>
>>>>>>>>>> a function is computable if there exists an algorithm
>>>>>>>>>> that can do the job of the function, i.e. given an input
>>>>>>>>>> of the function domain it can return the corresponding output.
>>>>>>>>>> https://en.wikipedia.org/wiki/Computable_function
>>>>>>>>>>
>>>>>>>>>> On Turing Machines inputs <are> finite strings, and
>>>>>>>>>> finite string transformation rules <are> applied to
>>>>>>>>>> these finite strings to derive corresponding outputs.
>>>>>>>>>>
>>>>>>>>> And it has been proven that no finite string transformations 
>>>>>>>>> are possible that report the halting behaviour for all inputs 
>>>>>>>>> that specify a correct program. 
>>>>>>>>
>>>>>>>> int sum(int x, int y) { return x + y; }
>>>>>>>> Only when people stupid assume the same thing as
>>>>>>>> sum(3,2) should return the sum of 5 + 3.
>>>>>>>>
>>>>>>> Therefore HHH should report on the actual input, the finite 
>>>>>>> string that describes a halting program. Not on the hypothetical 
>>>>>>> input that does not halt, because it is based on a hypothetical 
>>>>>>> HHH that does not abort.
>>>>>>>
>>>>>>> Why do you maintain that HHH should process the hypothetical 
>>>>>>> input instead of the actual input.
>>>>>>> Do you really believe that 3+2 equals 5+3?
>>>>>>
>>>>>> I have proven that the directly executed DD and DD
>>>>>> emulated by HHH according to the semantics of the
>>>>>> x86 language have a different set of state changes
>>>>>> many hundreds of times for several years.
>>>>> You never showed a proof. You only repeated a dream. You are 
>>>>> dreaming many years without any logic. You failed to show the first 
>>>>> state change where the direct execution is different from the 
>>>>> simulation. You only showed an erroneous HHH that fails to reach 
>>>>> the end of the simulation of a halting program.
>>>>
>>>> Worse than this, on more than one occasion I've actually posted 
>>>> traces of computation DDD(DDD) executed directly and simulated by 
>>>> HHH side by side.  Both traces were of course /identical/, up to the 
>>>> point where HHH stops simulating. 
>>>
>>> *Factually incorrect* (You are usually very careful about these things)
>>> The call to HHH(DD) from the directly executed DD returns.
>>> The call to HHH(DD) from DD emulated by HHH cannot possibly return.
>>>
>>
>> ...because HHH stops simulating before reaching that step in the 
>> computation.  Note that I said
>>
>> MT:  Both traces were of course /identical/,
>>       *up to the point where HHH stops simulating*
>>
>> So I was factually correct.
>>
>>
>> Mike.
>>
> 
> THEY DIFFER BY THE EMULATED DD REACHES RECURSIVE EMULATION
> AND THE DIRECTLY EXECUTED DD NEVER DOES.
> 
> 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.
> 

It is only a finite recursion. Only if you change the input as well, 
then it does not reach the end after an infinite number of steps. But 
for the input given to *this* HHH, which is DD that calls this HHH that 
aborts, only a finite number of steps is needed, but HHH does not 
simulate enough steps to see it. The programmer introduced a bug, which 
made HHH blind for finite recursions.