On 4/18/2023 10:10 PM, Richard Damon wrote:
> On 4/18/23 10:57 PM, olcott wrote:
>> On 4/18/2023 9:31 PM, Richard Damon wrote:
>>> On 4/18/23 7:13 PM, olcott wrote:
>>>> On 4/18/2023 5:30 PM, Richard Damon wrote:
>>>>> On 4/18/23 11:58 AM, olcott wrote:
>>>>>> On 4/18/2023 6:32 AM, Richard Damon wrote:
>>>>>>> On 4/18/23 1:00 AM, olcott wrote:
>>>>>>>> A simulating halt decider correctly predicts whether or not its
>>>>>>>> correctly simulated input can possibly reach its own final state
>>>>>>>> and
>>>>>>>> halt. It does this by correctly recognizing several non-halting
>>>>>>>> behavior
>>>>>>>> patterns in a finite number of steps of correct simulation.
>>>>>>>> Inputs that
>>>>>>>> do terminate are simply simulated until they complete.
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> Except t doesn't o this for the "pathological" program.
>>>>>>>
>>>>>>> The "Pathological Program" when built on such a Decider that does
>>>>>>> give an answer, which you say will be non-halting, and then
>>>>>>> "Correctly Simulated" by giving it representation to a UTM, we
>>>>>>> see that the simulation reaches a final state.
>>>>>>>
>>>>>>> Thus, your H was WRONG t make the answer. And the problem is you
>>>>>>> have added a pattern that isn't always non-halting.
>>>>>>>
>>>>>>>> When a simulating halt decider correctly simulates N steps of
>>>>>>>> its input
>>>>>>>> it derives the exact same N steps that a pure UTM would derive
>>>>>>>> because
>>>>>>>> it is itself a UTM with extra features.
>>>>>>>
>>>>>>> But if ISN'T a "UTM" any more, because some of the features you
>>>>>>> added have removed essential features needed for it to be an
>>>>>>> actual UTM. That you make this claim shows you don't actually
>>>>>>> know what a UTM is.
>>>>>>>
>>>>>>> This is like saying a NASCAR Racing Car is a Street Legal
>>>>>>> vehicle, since it started as one and just had some extra features
>>>>>>> axded.
>>>>>>>
>>>>>>>>
>>>>>>>> My reviewers cannot show that any of the extra features added to
>>>>>>>> the UTM
>>>>>>>> change the behavior of the simulated input for the first N steps
>>>>>>>> of simulation:
>>>>>>>> (a) Watching the behavior doesn't change it.
>>>>>>>> (b) Matching non-halting behavior patterns doesn't change it
>>>>>>>> (c) Even aborting the simulation after N steps doesn't change
>>>>>>>> the first N steps.
>>>>>>>
>>>>>>> No one claims that it doesn't correctly reproduce the first N
>>>>>>> steps of the behavior, that is a Strawman argumen.
>>>>>>>
>>>>>>>>
>>>>>>>> Because of all this we can know that the first N steps of input D
>>>>>>>> simulated by simulating halt decider H are the actual behavior
>>>>>>>> that D
>>>>>>>> presents to H for these same N steps.
>>>>>>>>
>>>>>>>> *computation that halts*… “the Turing machine will halt whenever
>>>>>>>> it enters a final state” (Linz:1990:234)rrr
>>>>>>>
>>>>>>> Right, so we are concerned about the behavior of the ACTUAL
>>>>>>> machine, not a partial simulation of it.
>>>>>>> H(D,D) returns non-halting, but D(D) Halts, so the answer is wrong.
>>>>>>>
>>>>>>>>
>>>>>>>> When we see (after N steps) that D correctly simulated by H cannot
>>>>>>>> possibly reach its simulated final state in any finite number of
>>>>>>>> steps
>>>>>>>> of correct simulation then we have conclusive proof that D
>>>>>>>> presents non-
>>>>>>>> halting behavior to H.
>>>>>>>
>>>>>>> But it isn't "Correctly Simulated by H"
>>>>>> You agreed that the first N steps are correctly simulated.
>>>>>>
>>>>>> It turns out that the non-halting behavior pattern is correctly
>>>>>> recognized in the first N steps.
>>>>>>
>>>>>
>>>>> Nope, the pattern you detect isn't a "Nobn-Halting" pattern, as is
>>>>> shown by the fact that D(D) does halt.
>>>>>
>>>>> It might show that no possible H could simulate the input to a
>>>>> final state, but that isn't the definition of Halting. Halting is
>>>>> strictly about the behavior of the machine itself.
>>>>
>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>
>>>> computation that halts… “the Turing machine will halt whenever it
>>>> enters
>>>> a final state” (Linz:1990:234)
>>>
>>> Right and Ĥ (Ĥ) will reach Ĥ.qn and halt if H (Ĥ) (Ĥ) goes to qn, as
>>> it must to be saying that its input is non-halting.
>>>
>>> This is because embedded_H and H must be identical machines, and thus
>>> do exactly the same thing when given the same input.
>>>
>>>>
>>>> Non-halting behavior patterns can be matched in N steps
>>>> ⟨Ĥ⟩ Halting is reaching its simulated final state of ⟨Ĥ.qn⟩ in a finite
>>>> number of steps
>>>
>>> Nope, Halting is the MACHINE Ĥ (Ĥ) reaching its final state Ĥ.qn in a
>>> finite number of steps.
>>>
>>> You can also use UTM (Ĥ) (Ĥ), which also reaches that final stste,
>>> because it doesn't stop simulating until it reaches a final state, or
>>> it just keeps simulating.
>>>
>>> H / embedded_H are NOT a UTM, as they don't have that necessary
>>> property.
>>>
>>>>
>>>> N steps of ⟨Ĥ⟩ correctly simulated by embedded_H are the actual
>>>> behavior of this input:
>>>> (a) Ĥ.q0 The input ⟨Ĥ⟩ is copied then transitions to embedded_H
>>>> (b) embedded_H is applied to ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy) which
>>>> simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>> (c) *which begins at its own simulated ⟨Ĥ.q0⟩ to repeat the process*
>>>
>>> Except you have defined that H, and thus embeded_H doesn't do (c),
>>> but when it sees the attempted to go into embedded_H with the same
>>> input actually aborts its simulation and goes to Ĥ.qn which causes
>>> the machine Ĥ to halt.
>>>
>>
>> embedded_H could do (c) 10,000 times before aborting which would have to
>> be the actual behavior of the actual input because embedded_H remains in
>> pure UTM mode until it aborts.
>
> No such thing. UTM isn't a "Mode" but an identity.
>
> if embedded_H aborts its simulation, it NEVER was a UTM. PERIOD.
But that is flat out not the truth. The input simulated by embedded_H
necessarily must have exact same behavior as simulated by a pure UTM
until the simulation of this input is aborted because aborting the
simulation of its input is the only one of three features added to a UTM
that changes the behavior of its input relative to a pure UTM.

(a) Watching the behavior doesn't change it.
(b) Matching non-halting behavior patterns doesn't change it.
(b) Even aborting the simulation after N steps doesn't change the first
N steps.

N steps could be 10,000 recursive simulations.

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