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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Every sufficiently competent C programmer knows --- Truthmaker
 Maximalism
Date: Fri, 14 Mar 2025 21:34:36 -0400
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On 3/14/2025 9:27 PM, olcott wrote:
> On 3/14/2025 8:00 PM, dbush wrote:
>> On 3/14/2025 8:45 PM, olcott wrote:
>>> On 3/14/2025 12:54 PM, dbush wrote:
>>>> On 3/14/2025 12:33 PM, olcott wrote:
>>>>> On 3/14/2025 11:01 AM, wij wrote:
>>>>>> On Fri, 2025-03-14 at 10:51 -0500, olcott wrote:
>>>>>>> On 3/14/2025 10:04 AM, wij wrote:
>>>>>>>> On Fri, 2025-03-14 at 09:35 -0500, olcott wrote:>>
>>>>>>>>> void DDD()
>>>>>>>>> {
>>>>>>>>>      HHH(DDD);
>>>>>>>>>      return;
>>>>>>>>> }
>>>>>>>>>
>>>>>>>>> DDD correctly simulated by HHH cannot possibly reach
>>>>>>>>> its own "return" instruction in any finite number of
>>>>>>>>> correctly simulated steps.
>>>>>>>>>
>>>>>>>>> That you are clueless about the semantics of something
>>>>>>>>> as simple as a tiny C function proves that you are not
>>>>>>>>> competent to review my work.
>>>>>>>>>
>>>>>>>>
>>>>>>>> https://en.wikipedia.org/wiki/Halting_problem
>>>>>>>> In computability theory, the halting problem is the problem of 
>>>>>>>> determining, from a description of
>>>>>>>> an
>>>>>>>> arbitrary computer program and an input, whether the program 
>>>>>>>> will finish running, or continue to
>>>>>>>> run
>>>>>>>> forever.
>>>>>>>>
>>>>>>>> That means: H(D)=1 if D() halts and H(D)=0 if D() does not halt.
>>>>>>>>
>>>>>>>> But, it seems you don't understand English, as least as my 
>>>>>>>> level, ....
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> void DDD()
>>>>>>> {
>>>>>>>     HHH(DDD);
>>>>>>>     return;
>>>>>>> }
>>>>>>>
>>>>>>> The only difference between HHH and HHH1 is that they are
>>>>>>> at different locations in memory. DDD simulated by HHH1
>>>>>>> has identical behavior to DDD() directly executed in main().
>>>>>>>
>>>>>>> The semantics of the finite string input DDD to HHH specifies
>>>>>>> that it will continue to call HHH(DDD) in recursive simulation.
>>>>>>>
>>>>>>> The semantics of the finite string input DDD to HHH1 specifies
>>>>>>> to simulate to DDD exactly once.
>>>>>>>
>>>>>>> When HHH(DDD) reports on the behavior that its input finite
>>>>>>> string specifies it can only correctly report non-halting.
>>>>>>>
>>>>>>> When HHH(DDD) is required to report on behavior other than
>>>>>>> the behavior that its finite string specifies HHH is not
>>>>>>> a decider thus not a halt decider.
>>>>>>>
>>>>>>> All deciders are required to compute the mapping from
>>>>>>> their input finite string to the semantic or syntactic property
>>>>>>> that this string specifies. Deciders return true when this
>>>>>>> string specifies this property otherwise they return false.
>>>>>>>
>>>>>>
>>>>>> Are you solving The Halting Problem or not? Yes or No.
>>>>>>
>>>>>>
>>>>>
>>>>> I have only correctly refuted the conventional halting
>>>>> problem proof. 
>>>>
>>>> And what exactly do you think this proof is proving?  More 
>>>> specifically, what do you think the Linz proof is proving?
>>>
>>> All of the proofs merely show that there cannot
>>> possibly exist any halt decider that returns a
>>> value corresponding to the behavior of any input
>>> that is actually able to do the opposite of whatever
>>> value is returned.
>>>
>> Not exactly.  What they prove is that no H exists that satisfies these 
>> requirements:
>>
>>
>> Given any algorithm (i.e. a fixed immutable sequence of instructions) 
>> X described as <X> with input Y:
>>
>> A solution to the halting problem is an algorithm H that computes the 
>> following mapping:
>>
>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed 
>> directly
>>
> 
> The executed directly part is bogus as I have
> shown and your indoctrination blindly ignores.
> 

But I want to know if any arbitrary X with input Y halts when executed 
directly, and having an H that can compute that in ALL possible cases 
would be *very* useful to me.  If I had such an H, I could use it to 
solve the Goldbach conjecture.  And for this reason, everyone else wants 
such an H.

In contract, having an H that tells us if X simulated by H halts is 
*not* useful.