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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: The philosophy of computation reformulates existing ideas on a
 new basis
Date: Sat, 9 Nov 2024 08:56:14 -0600
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On 11/9/2024 3:53 AM, Mikko wrote:
> On 2024-11-08 14:39:20 +0000, olcott said:
> 
>> On 11/8/2024 6:39 AM, Mikko wrote:
>>> On 2024-11-07 16:39:57 +0000, olcott said:
>>>
>>>> On 11/7/2024 3:56 AM, Mikko wrote:
>>>>> On 2024-11-06 15:26:06 +0000, olcott said:
>>>>>
>>>>>> On 11/6/2024 8:39 AM, Mikko wrote:
>>>>>>> On 2024-11-05 13:18:43 +0000, olcott said:
>>>>>>>
>>>>>>>> On 11/5/2024 3:01 AM, Mikko wrote:
>>>>>>>>> On 2024-11-03 15:13:56 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 11/3/2024 7:04 AM, Mikko wrote:
>>>>>>>>>>> On 2024-11-02 12:24:29 +0000, olcott said:
>>>>>>>>>>>
>>>>>>>>>>>> HHH does compute the mapping from its input DDD
>>>>>>>>>>>> to the actual behavior that DDD specifies and this
>>>>>>>>>>>> DOES INCLUDE HHH emulating itself emulating DDD.
>>>>>>>>>>>
>>>>>>>>>>> Yes but not the particular mapping required by the halting 
>>>>>>>>>>> problem.
>>>>>>>>>>
>>>>>>>>>> Yes it is the particular mapping required by the halting problem.
>>>>>>>>>> The exact same process occurs in the Linz proof.
>>>>>>>>>
>>>>>>>>> The halting probelm requires that every halt decider terminates.
>>>>>>>>> If HHH(DDD) terminates so does DDD. The halting problmen requires
>>>>>>>>> that if DDD terminates then HHH(DDD) accepts as halting.
>>>>>>>>
>>>>>>>> void Infinite_Loop()
>>>>>>>> {
>>>>>>>>    HERE: goto HERE;
>>>>>>>>    return;
>>>>>>>> }
>>>>>>>>
>>>>>>>> No that is false.
>>>>>>>> The measure is whether a C function can possibly
>>>>>>>> reach its "return" instruction final state.
>>>>>>>
>>>>>>> Not in the original problem but the question whether a particular 
>>>>>>> strictly
>>>>>>> C function will ever reach its return instruction is equally 
>>>>>>> hard. About
>>>>>>
>>>>>> It has always been about whether or not a finite string input
>>>>>> specifies a computation that reaches its final state.
>>>>>
>>>>> Not really. The original problem was not a halting problem but 
>>>>> Turing's
>>>>
>>>> Exactly. The actual Halting Problem was called that by Davis
>>>> in 1952. Not the same as Turing proof.
>>>
>>> In early times there was variation in how things were presented and what
>>> words were used. Post had studied the halting problem of his tag system
>>> much earlier but didn't call it a machine. Many other problems were also
>>> studied and later found to be more or less related to the halting
>>> problem and its variants.
>>>
>>>> *So we are back to The Halting Problem itself*
>>>>
>>>> has always been about whether or not a finite string input
>>>> specifies a computation that reaches its final state.
>>>
>>> No, it has been a collection of related problems that includes that
>>> particular one.
>>
>> The halting problem has always been abuut halting
> 
> Nevertheless Turing's solution to his circularity problem is usually
> regarded as the first solution to the halting problem.
> 
>>> As the problems are related and equally hard it does
>>> not really matter which one you choose as long as you are clear
>>> about your choice. To argue about the meaning of words id a clear
>>> indcation of an intent to avoid an honest discussion.
> 
>> It is not the meaning of words it is the semantic
>> property of the finite string pair HHH/DDD.
> 
> Above you have argued about the meanings of the words and
> keep doing so below.
> 

It is the meaning of the bytes of x86 code and
bytes of code are not words.

>> The halting problem has always been about whether a finite
>> string input specifies a computation that will reach its
>> final halt state.
>>
>> If you disagree then you must provide a complete and coherent
>> counter-example conclusively proving otherwise not merely
>> some vague reference to some other things somewhere else.
> 
>  From https://www.tutorialspoint.com/automata_theory/ 
> turing_machine_halting_problem.htm
> 
>> Turing Machine Halting Problem
>> Input − A Turing machine and an input string w.
>> Problem − Does the Turing machine finish computing of the string w in 
>> a finite number of steps? The answer must be either yes or no.

The computation specified by the finite string DDD
emulated by HHH cannot possibly reach its "return"
instruction final halt state.

The computation specified by the finite string DDD
emulated by HHH1 IS NOT THE ACTUAL INPUT TO HHH.

HHH must compute the mapping FROM ITS INPUT TO THE
BEHAVIOR THAT THIS INPUT SPECIFIES.


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer