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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: The philosophy of computation reformulates existing ideas on a
 new basis
Date: Mon, 11 Nov 2024 10:53:28 -0500
Organization: i2pn2 (i2pn.org)
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On 11/11/24 10:15 AM, olcott wrote:
> On 11/11/2024 5:06 AM, Mikko wrote:
>> On 2024-11-09 14:56:14 +0000, olcott said:
>>
>>> 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.
>>
>> No, nothing you have said tells anuything about meanings of the bytes
>> of x86 code. (A pair of such bytes is sometimes called a "word").
>> You were just arguing about the meanings the verb "halt" and other
>> words.
>>
> 
> Halt means reaching a final halt state to say otherwise
> is ignorant or dishonest.

And not halting means never reaching that final state after an unbounded 
number of steps.

Showing it didn't yet halt after a finite number of steps doesn't show 
non-halting, just didn't halt yet.

> 
>>>>> 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.
>>
>> It can and does if HHH is a decider and otherwise does not matter.
>>
> 
> _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]
> 
> HHH is a correct termination analyzer that does correctly
> determine that DDD emulated by HHH cannot possibly reach
> its own [00002183] machine address.

No, it is an INCORRECT terminatation analyzer that INCORRECRTLY 
determines that DDD will not terminate.

DDD emulated by HHH is NOT a valid condition to base termination 
analysis, so, you are just showing you don't know what you are talking 
about.

> 
> The erroneous assumptions about halt deciders are anchored
========== REMAINDER OF ARTICLE TRUNCATED ==========