XPost: comp.theory
From: chris.m.thomasson.1@gmail.com
On 10/29/2025 10:21 AM, Kaz Kylheku wrote:
> On 2025-10-29, olcott wrote:
>> On 10/29/2025 12:36 AM, Kaz Kylheku wrote:
>>> On 2025-10-29, olcott wrote:
>>>> On 10/28/2025 9:19 PM, Kaz Kylheku wrote:
>>>>> On 2025-10-29, olcott wrote:
>>>>>> On 10/28/2025 7:25 PM, Kaz Kylheku wrote:
>>>>>>> Under your system, I don't know whether Y is correct.
>>>>>>>
>>>>>>> Y could be a broken decider that is wrongly deciding D (and /that/
>>>>>>> is why its execution trace differs from X).
>>>>>>>
>>>>>>> Or it could be the case that D is a non-input to Y, in which case Y is
>>>>>>> deemed to be correct because D being a non-input to Y means that D
>>>>>>> denotes non-halting semantics to Y (and /that/ is why its execution
>>>>>>> trace differs from X).
>>>>>>>
>>>>>>> The fact that the execution trace differs doesn't inform.
>>>>>>>
>>>>>>> We need to know the value of is_input(Y, D): we need to /decide/
whether
>>>>>>> D is non-input or input to Y in order to /decide/ whether its rejection
>>>>>>> is correct.
>>>>>>>
>>>>>>
>>>>>> Whatever is a correct simulation of an input by
>>>>>> a decider is the behavior that must be reported on.
>>>>>
>>>>> But under your system, if I am a user of deciders, and have been
>>>>> given a decider H which is certified to be correct, I cannot
>>>>> rely on it to decide halting.
>>>>>
>>>>
>>>> When halting is defined correctly:
>>>> Does this input specify a sequence of moves that
>>>> reach a final halt state?
>>>>
>>>> and not defined incorrectly: to require something
>>>> that is not specified in the input then this does
>>>> overcome the halting problem proof and shows that
>>>> the halting problem itself has always been a category
>>>> error. (Flibble's brilliant term).
>>>>
>>>>> I want to know whether D halts, that's all.
>>>>>
>>>>> H says no. It is certified correct under your paradigm, so
>>>>> so I don't have to suspect that if it is given an /input/
>>>>> it will be wrong.
>>>>>
>>>>> But: I have no idea whether D is an input to H or a non-input!
>>>>>
>>>>
>>>> That is ridiculous. If it is an argument
>>>> to the decider function then it is an input.
>>>
>>> So how it's supposed to work that an otherwise halting D
>>> is a non-halting input to H.
>>>
>>
>> int D()
>> {
>> int Halt_Status = H(D);
>> if (Halt_Status)
>> HERE: goto HERE;
>> return Halt_Status;
>> }
>>
>> H simulates D
>> that calls H(D) to simulate D
>> that calls H(D) to simulate D
>> that calls H(D) to simulate D
>> that calls H(D) to simulate D
>> that calls H(D) to simulate D
>> until H sees this repeating pattern.
>>
>>> When the non-halting D is an input to H (which it undeniably as you have
>>> now decided) D is non-halting.
>>>
>>
>> D.input_to_H is non-halting is confirmed in that
>> D simulated by cannot possibly reach its own
>> "return" statement final halt state. This divides
>> non-halting from stopping running.
>>
>>> With respect to H, it's as if the halting D exists in another dimension;
>>> /that/ D is not the input.
>>>
>>> Okay, but anyway ...
>>>
>>> - The decider user has some program P..
>>>
>>> - P terminates, but it takes three years on the user's hardware.
>>>
>>> - The user does not know this; they tried running P for weeks,
>>> months, but it never terminated.
>>>
>>> - The user has H which they have been assured is correct under
>>> the Olcott Halting Paradigm.
>>>
>>> - The applies H to P, and H rejects it.
>>>
>>
>> The would mean that P has specifically targeted
>> H in an attempt to thwart a correct assessment.
>>
>>> - The program P is actually D, but the user doesn't know this.
>>>
>>
>> The system works on source-code.
>
> Whatever results you have, they have to be valid
> for any representation of Turing machines whatsoever.
>
> Source code can be obfuscated, as well as extremely large and
> obfuscated.
>
> That the user can have source code (not required at all by the Turing
> model) doesn't change that the user has no idea that P is actually a D
> program with respect to their halting decider.
>
> Also, the question "is this input P a diagonal input targetin this
> decider H" is an undecidable problem!!!
>
>>> What should the user believe? Does D halt or not?
>>>
>>
>> When the input P targets the decider H or does not target
>> the decider H input P simulated by decider H always reports
>> on the basis of whether P can reach its own final halt state.
>
> But that's not the output we want; we want to know whether P()
> halts.
>
>>> How is the user /not/ deceived if they believe that P doesn't halt?
>>>
>>>>> When H says 0, I have no idea whether it's being judged non-halting
>>>>> as an input, or whether it's being judged as a non-input (whereby
>>>>> either value is the correct answer as far as H is concerned).
>>>>>
>>>>
>>>> Judging by anything besides and input has always
>>>> been incorrect. H(D) maps its input to a reject
>>>> value on the basis of the behavior that this
>>>> argument to H specifies.
>>>
>>> But that behavior is only real /as/ an argument to H; it is not the
>>> behavior that the halter-decider customer wants reported on.
>>>
>>
>> When what the customer wants and what is in the scope of
>> Turing machines differ the user must face reality.
>
> So under your paradigm, the user is told they must face reality: some
> machines cannot be decided, so you cannot get an answer for whether P()
> halts. Sometimes you get answer for whether P is considered to be
> halting when simulated by H, which doesn't match whether P() halts. Suck
> it up!
>
> That's just a stupidly convoluted version of what they are told
> under the standard Halting Problem, which informs them that for
> every halting decider, there are inputs for which it is wrong or
> nonterminating.
>
> You are not improving the standard halting problem and its theorem
> one iota; just vandalizing it with impertinent content and details.
>
> Under your paradigm, a halting decider reports rubbish for some inputs,
> and is called correct; e.g. rejecting a halting input.
>
> How is what you are doing different from calling a tail "leg",
> and claiming that canines are five-legged animals?
Indeed. Actually, it reminds me of the art on the cover of the following
game:
https://en.wikipedia.org/wiki/Nord_and_Bert_Couldn%27t_Make_Head_or_Tail_of_It
A cow with two asses? I can say head up own ass and might beat a puzzle.
lol.
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