On 1/3/2022 12:59 PM, Richard Damon wrote:
>
> On 1/3/22 1:26 PM, olcott wrote:
>> On 1/3/2022 12:18 PM, Richard Damon wrote:
>>>
>>> On 1/3/22 12:37 PM, olcott wrote:
>>>> On 1/3/2022 11:10 AM, Richard Damon wrote:
>>>>> On 1/3/22 11:53 AM, olcott wrote:
>>>>>> On 1/3/2022 10:43 AM, Richard Damon wrote:
>>>>>>> On 1/3/22 11:34 AM, olcott wrote:
>>>>>>>> On 1/3/2022 9:28 AM, Richard Damon wrote:
>>>>>>>>>
>>>>>>>>> On 1/3/22 10:24 AM, olcott wrote:
>>>>>>>>>> On 1/3/2022 9:18 AM, Richard Damon wrote:
>>>>>>>>>>>
>>>>>>>>>>> On 1/3/22 9:25 AM, olcott wrote:
>>>>>>>>>>>> Revised Linz H halt deciding criteria (My criteria Ben's
>>>>>>>>>>>> notation)
>>>>>>>>>>>> H.q0 wM w ⊢* H.qy iff UTM(wM, w) halts
>>>>>>>>>>>> H.q0 wM w ⊢* H.qn iff UTM(wM, w) does not halt
>>>>>>>>>>>>
>>>>>>>>>>>> The above means that the simulating halt decider H bases its
>>>>>>>>>>>> halt status decision on the behavior of the pure UTM
>>>>>>>>>>>> simulation of its input.
>>>>>>>>>>>>
>>>>>>>>>>>> H examines this behavior looking for infinite behavior
>>>>>>>>>>>> patterns. When H detects an infinite behavior pattern it
>>>>>>>>>>>> aborts the simulation of its input and transitions to H.qn.
>>>>>>>>>>>
>>>>>>>>>>> This pattern does not exist as a finite pattern.
>>>>>>>>>>>
>>>>>>>>>>> Proved, and accepted by failure to rebut.
>>>>>>>>>>>
>>>>>>>>>>> Mesage ID  <FOnzJ.162569$np6.119786@fx46.iad>
>>>>>>>>>>> Date: 2021-12-30 19:31:49 GMT
>>>>>>>>>>> Subject: Re: Concise refutation of halting problem proofs V42
>>>>>>>>>>> [compute the mapping]
>>>>>>>>>>>
>>>>>>>>>>> FAIL.
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Infinite behavior patterns are cases where the the pure UTM
>>>>>>>>>>>> simulation of the input would never reach the final state of
>>>>>>>>>>>> this input.
>>>>>>>>>>>>
>>>>>>>>>>>> For simplicity we will refer to the copy of Linz H at Ĥ.qx
>>>>>>>>>>>> embedded_H.
>>>>>>>>>>>>
>>>>>>>>>>>> Simplified syntax adapted from bottom of page 319:
>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>
>>>>>>>>>>>> When embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩ these steps would keep
>>>>>>>>>>>> repeating:
>>>>>>>>>>>> Ĥ copies its input ⟨Ĥ⟩ to ⟨Ĥ⟩ then embedded_H simulates ⟨Ĥ⟩
>>>>>>>>>>>> ⟨Ĥ⟩...
>>>>>>>>>>>>
>>>>>>>>>>>> This shows that the input to embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ would never
>>>>>>>>>>>> reach its final state thus conclusively proving that this
>>>>>>>>>>>> input never halts.
>>>>>>>>>>>> This enables embedded_H to correctly transition to Ĥ.qn.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> WRONG.
>>>>>>>>>> LIAR !!!
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> PROVE IT, or YOUR the LIAR.
>>>>>>>>>
>>>>>>>>> I have shown my proof, which you have failed to give a rebuttal
>>>>>>>>> that actually tries to rebut it.
>>>>>>>>>
>>>>>>>>> IF embedded_H doesn't abort, then H never gets to Qn as claimed
>>>>>>>>>
>>>>>>>>> If embedded_H does abort and go to Qn, then H^ also goes to Qn
>>>>>>>>> and Halts.
>>>>>>>>
>>>>>>>> embedded_H is only accountable for mapping the behavior of the
>>>>>>>> pure simulation of its input ⟨Ĥ⟩ ⟨Ĥ⟩ to an accept / reject state.
>>>>>>>
>>>>>>> Right, and to correctly answer the input <H^> <H^> then
>>>>>>> H/embedded_H must go to the state that matches the behavior of
>>>>>>> the Computation of H^ applied to <H^>.
>>>>>>>
>>>>>>
>>>>>> WRONG:
>>>>>> embedded_H must go to the state that correctly describes the
>>>>>> behavior of the pure simulation of the input to embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>
>>>>>> these steps would keep repeating:
>>>>>> Ĥ copies its input ⟨Ĥ⟩ to ⟨Ĥ⟩ then embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩...
>>>>>>
>>>>>
>>>>> That only happens if embedded_H never aborts its simulation of its
>>>>> input.
>>>>>
>>>>> And if that happens, it can never then abort and go to Qn to be
>>>>> 'right', as all copies of an algorithm when given the same input
>>>>> behave the same.
>>>>>
>>>> The criteria that H uses is what the behavior would be if H never
>>>> aborted the simulation of its input.
>>>>
>>>
>>> Which is gthe WRONG criteria!!!!
>>>
>>> THe criteria NEEDS to be what is the behavior of the machine the
>>> input represents, or of a REAL UTM given that same input.
>>>
>>> So, THERE'S YOUR PROBLEM!
>>
>> The criteria of H is whether or not the pure simulation of its input
>> would ever reach its final state. The pure simulation of the input to
>> embedded_H would never reach its final state.
>
> This was just explained to you.
>
> IF you actually mean this, then that means that H has to be defined as
> never going to H.qn, as if it does, then the pure simulation of it input
> will end up stopping in H^.qn
>

As I keep telling you and you keep stupidly ignoring the fact that the
input stops running because its simulation was aborted is no indication
what-so-ever that this simulated input halts. HALTING IS ONLY REACHING A
FINAL STATE.

You also stupidly ignore that the halt decider is only accountable for
what the behavior of its actual input would be. It is not responsible
for the behavior of any non-inputs.

> FAIL.
>
>>
>>>> You seem to be confused into believing that when H aborts the
>>>> simulation of its input that this causes the input to halt. This is
>>>> not true. An input only halts when it reaches its final state.
>>>>
>>>
>>> But it isn't the 'input' that matters, but the computation that the
>>> input represents, and since that computation uses a copy of H, the
>>> behavior of the computation is depencent on what H does, and if H
>>> goes to Qn then it Halts. PERIOD.
>>>
>>> This is one of your old errors that shows that you don't understand
>>> what you are talking about.
>>>
>>>> As long as the input would never reach its final state if H did not
>>>> abort the simulation of its input then H is ALWAYS free to abort its
>>>> simulation and correctly transition to H.qn.
>>>
>>> By THAT definitions, ANY input could be correctly decided non-halting
>>> by a 'simulating decider that just immediately aborts its
>>> simulation', which is non-sense.
>>
>> NO STUPID THAT IS NOT WHAT THIS MEANS:
>> As long as the input would never reach its final state if H did not
>> abort the simulation of its input
>>
>
> WRONG. You are using the wrong definition AGAIN.
>
> Show me where the definition for the Halting Decider says 'if H did not
> abort its simulation of its input'.
>

THAT IS WHAT THIS MEANS:
H.q0 wM w ⊢* H.qy iff UTM(wM, w) halts
H.q0 wM w ⊢* H.qn iff UTM(wM, w) does not halt

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer