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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: Wed, 13 Nov 2024 20:09:24 -0500
Organization: i2pn2 (i2pn.org)
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On 11/13/24 6:08 PM, olcott wrote:
> 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.

But not all "C Functions" have semantic properties. Only leaf functions, 
or functions made to be leaf functions by including the code they call.

And, once you add to your "C Function" DDD, the HHH that it actually 
calls, that is the HHH that returns the answer, we see that the semantic 
property of reaching the end will be satisfied by that DDD.

> 
>>>> 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.

And only the COMPLETE emulation determines its behavior.

Since the HHH that answers doesn't do that, its emulation is not 
determinative, but only the emulation of another emulator, given the 
EXACT SAME FULL PROGRAM as HHH had, that is the DDD that calls that HHH 
that aborts, and such an emulator WILL reach the final state, as HHH1 shows.

> 
>>> 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.
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