On 1/25/2023 5:29 PM, olcott wrote:
> On 1/25/2023 5:15 PM, Richard Damon wrote:
>> On 1/25/23 11:51 AM, olcott wrote:
>>> On 1/25/2023 5:46 AM, Richard Damon wrote:
>>>> On 1/25/23 12:13 AM, olcott wrote:
>>>>> On 1/24/2023 10:09 PM, Richard Damon wrote:
>>>>>> On 1/24/23 10:51 PM, olcott wrote:
>>>>>>> On 1/24/2023 9:40 PM, Richard Damon wrote:
>>>>>>>> On 1/24/23 10:10 PM, olcott wrote:
>>>>>>>>> On 1/24/2023 8:03 PM, Richard Damon wrote:
>>>>>>>>>> On 1/24/23 7:26 PM, olcott wrote:
>>>>>>>>>>> On 1/24/2023 5:41 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/24/23 10:41 AM, olcott wrote:
>>>>>>>>>>>>> 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.  https://en.wikipedia.org/wiki/Halting_problem
>>>>>>>>>>>>>
>>>>>>>>>>>>> This definition of the halting problem measures correctness
>>>>>>>>>>>>> in a non-
>>>>>>>>>>>>> pathological way, thus in the same way that ZFC (redefined
>>>>>>>>>>>>> set theory
>>>>>>>>>>>>> and) eliminated Russell's Paradox the previously
>>>>>>>>>>>>> "impossible" input
>>>>>>>>>>>>> ceases to be impossible.
>>>>>>>>>>>>>
>>>>>>>>>>>>> In computability theory, the halting problem is the problem
>>>>>>>>>>>>> of defining
>>>>>>>>>>>>> a machine that correctly determines from a description of
>>>>>>>>>>>>> an arbitrary
>>>>>>>>>>>>> computer program and an input, whether or not its specified
>>>>>>>>>>>>> input pair
>>>>>>>>>>>>> would terminate normally by reaching it own final state.
>>>>>>>>>>>>
>>>>>>>>>>>> Right, the Decider must decide if the actual running of the
>>>>>>>>>>>> program described by the input would halt when given the
>>>>>>>>>>>> input that is the rest of that input.
>>>>>>>>>>>>
>>>>>>>>>>>> It is NOT asking if the
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> The conventional proofs do not actually show that such a
>>>>>>>>>>>>> machine cannot
>>>>>>>>>>>>> be defined. HH(PP, PP) does correctly determine that its
>>>>>>>>>>>>> correctly
>>>>>>>>>>>>> simulated input cannot possibly reach the final state of PP
>>>>>>>>>>>>> and
>>>>>>>>>>>>> terminate normally. (See pages 5-6 of this paper)
>>>>>>>>>>>>>
>>>>>>>>>>>>> https://www.researchgate.net/publication/364657019_Simulating_Halt_Decider_Applied_to_the_Halting_Theorem
>>>>>>>>>>>>>
>>>>>>>>>>>>> If the simulation is incorrect then there must a line of
>>>>>>>>>>>>> the simulation
>>>>>>>>>>>>> that behaves differently than what its corresponding line
>>>>>>>>>>>>> of machine-
>>>>>>>>>>>>> code specifies.
>>>>>>>>>>>>
>>>>>>>>>>>> No, it is incorrect because it is incomplete.
>>>>>>>>>>>>
>>>>>>>>>>>> You are just usong the INCORRECT definition of "Correct",
>>>>>>>>>>>> and since you have been told this in the past, it just shows
>>>>>>>>>>>> that you are a LIAR about this fact.
>>>>>>>>>>>>
>>>>>>>>>>>> "Correct Simulation" is defined as a simulation that exactly
>>>>>>>>>>>> matches the actual behavior of the machine the input describes.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> It turns out that is incorrect. The ultimate measure of a
>>>>>>>>>>> correct
>>>>>>>>>>> simulation is whether or not the simulated input exactly
>>>>>>>>>>> matches the
>>>>>>>>>>> behavior specified by its machine code.
>>>>>>>>>>
>>>>>>>>>> Nope, Sourcd for that claim.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Counter-examples cannot possibly exist.
>>>>>>>>> Try and show any correct simulation where the simulator does
>>>>>>>>> not simulate what the machine language specifies.
>>>>>>>>
>>>>>>>> This is the counter example.
>>>>>>>>
>>>>>>>> Since the direct eecution of the machine language of PP(PP) will
>>>>>>>> Halt, the correct simulation of it must match.
>>>>>>>>
>>>>>>>
>>>>>>> That is merely a provably false assumption.
>>>>>>
>>>>>> Then do so.
>>>>>>
>>>>>> Remember, your HH has been admitted to return 0 from HH(PP,PP),
>>>>>> and to be a computation, it must do the same to EVERY call.
>>>>>>
>>>>>> YOU have posted the execution trace of the direct execution of the
>>>>>> equivalent to PP, which shows it halts.
>>>>>>
>>>>>
>>>>> You can see on pages 5-6 that PP correctly simulated by HH cannot
>>>>> possibly reach it own final state.
>>>>
>>>> But that isn't the questipon, since that question, like the Liar's
>>>> paradox has no answer.
>>>>
>>> That makes the Halting Problem ill-defined:
>>
>> No, your RESTATEMENT is ill-defined. The behavior of P is well defined
>> given a proper definition of H
>>
>> H(P,P) can do one of 4 things, and can't do anything else.
>>
>> 1) H(P,P) can return 0, in which case P(P) will halt, and H is shown
>> to be wrong. This is what you claim your H does when directly called.
>>
>> 2) H(P,P) can retrun 1, in which case, P(P) will go into an infinite
>> loop, and H is shown to be wrong.
>>
>> 3) H(P,P) can just dies and halt and not return an answer, in which
>> case H fails to be the needed halt decider, and P(P) will be halting.
>>
>> 4) H(P,P) can get stuck in an infinte loop, and never return an
>> answer, in which case H fails to be the needed halt decider, and P(P)
>> will be non-halting. This is what you seem to claim is what H does
>> when simulated inside P.
>>
>>>
>>> In the study of problem solving, any problem in which the initial
>>> state or starting position, the allowable operations, and the goal
>>> state are clearly specified, *and a unique solution can be shown to
>>> exist*
>>
>> Right, and given an actual definition of the complete algorithm of H
>> (and 'Get the right answer' is NOT an complete algorithm) there is a
>> precise correct answer to the problem.
>>
>> Unfortunately of H, H can never give that answer.
>
> Thus making the halting problem ill-defined.

No machine can possibly be defined that divides all pairs of finite
strings into those that represent machines would halt on their input
when directly executed and those that do not in the same way and for the
same reason that there is no barber that shaves all and only those that
do not shave themselves. ZFC eliminated this problem by declaring it is
erroneous.

Every decision problem where
*a unique solution CANNOT be shown to exist*
is erroneous.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer