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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: The philosophy of computation reformulates existing ideas on a new basis
Date: Thu, 14 Nov 2024 11:06:11 +0200
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On 2024-11-13 23:08:40 +0000, olcott said:

> On 11/13/2024 4:54 AM, Mikko wrote:
>> On 2024-11-12 22:45:10 +0000, olcott said:
>> 
>>> On 11/12/2024 5:22 AM, Mikko wrote:
>>>> On 2024-11-11 15:15:09 +0000, olcott said:
>>>> 
>>>>> 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.
>>>> 
>>>> The exact definition of "halt" varies depending on the model.
>>>> For a Turing machine halting means reaching a configuration
>>>> where where there is no rule for the state and current symbol.
>>> 
>>> Since we are only talking about Turing Machines and C functions
>>> there is no need to get into other models.
>> 
>> You have also talked about x86, so it is better to include that.
> 
> That is construed as the precise details of the behavior
> of the C function.

Doing so deviates from the meaning of "C language".

>>>> For a C program it is more ambiguous as there are situations
>>>> where the language standard does not specify whether the execution
>>>> should be terminated or continued.
>>> 
>>> Reaching the "return" instruction final halt state <is>
>>> the only normal termination for a C function.
>> 
>> You may call it "only normal termitaion" but there are other terminations
>> that need not be called "normal".
> 
> When we preserve the mapping to Turing machines then
> reaching the return instruction is the only correct
> notion of a final halt state.

No, it is not. If you want to use the expression "final halt state"
about Turing machines you must define it in terms of Turing macnine
concepts, either as halting or as someting else.

>>> If you want to get silly you can say that a C function stuck
>>> in an infinite loop "halts" when you yank the computer's power
>>> cord out.
>> 
>> That is in the same category as the "aboting" your HHH may do with
>> certain inputs. The program does specify a next action but the
>> specified action is not performed.
> 
> No it is not. A emulating termination analyzer is
> defined to abort as soon as aborting is the only way
> to prevent its own non-termination.

If for a particular input aborting is the only way to prevent its own
non-termination then "as soon as" can only mean before doing anything
and therefore before finding out that there is no other way.

-- 
Mikko