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computers / comp.ai.philosophy / Re: Refuting the Peter Linz Halting Problem Proof V5 [ correct criteria ]

Re: Refuting the Peter Linz Halting Problem Proof V5 [ correct criteria ]
  comp.theory comp.ai.philosophy sci.logic sci.math
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Subject: Re: Refuting the Peter Linz Halting Problem Proof V5 [ correct
criteria ]
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From: NoOne@NoWhere.com (olcott)
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Xref: rslight2 comp.ai.philosophy:8185
 by: olcott - Thu, 24 Mar 2022 15:53 UTC

On 3/24/2022 10:30 AM, Richard Damon wrote:
> On 3/24/22 10:57 AM, olcott wrote:
>> On 3/24/2022 6:12 AM, Richard Damon wrote:
>>> On 3/23/22 11:05 PM, olcott wrote:
>>>> On 3/23/2022 9:31 PM, Richard Damon wrote:
>>>>>
>>>>> On 3/23/22 10:01 PM, olcott wrote:
>>>>>> On 3/23/2022 8:39 PM, Richard Damon wrote:
>>>>>>> On 3/23/22 9:29 PM, olcott wrote:
>>>>>>>> On 3/23/2022 7:15 PM, Richard Damon wrote:
>>>>>>>>> On 3/23/22 7:50 PM, olcott wrote:
>>>>>>>>>> On 3/23/2022 6:26 PM, Richard Damon wrote:
>>>>>>>>>>> On 3/23/22 7:20 PM, olcott wrote:
>>>>>>>>>>>> On 3/23/2022 6:04 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 3/23/22 9:09 AM, olcott wrote:
>>>>>>>>>>>>>> On 3/23/2022 6:19 AM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 3/23/22 12:00 AM, olcott wrote:
>>>>>>>>>>>>>>>> On 3/22/2022 10:37 PM, Ben Bacarisse wrote:
>>>>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> On 3/22/2022 9:32 AM, Ben Bacarisse wrote:
>>>>>>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> On 3/21/2022 10:22 PM, Ben Bacarisse wro0te:
>>>>>>>>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> A copy of Linz H is embedded at Ĥ.qx as a
>>>>>>>>>>>>>>>>>>>>>> simulating halt decider (SHD).
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>>>>>>>>>>>>>>>>>>> If the pure simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by embedded_H
>>>>>>>>>>>>>>>>>>>>>> would reach its final state.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>> If the pure simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by embedded_H
>>>>>>>>>>>>>>>>>>>>>> would never reach its
>>>>>>>>>>>>>>>>>>>>>> final state.
>>>>>>>>>>>>>>>>>>>>> But for your "PO-machines":
>>>>>>>>>>>>>>>>>>>>>      "Ĥ.qx maps ⟨Ĥ⟩ ⟨Ĥ⟩ to Ĥ.qn
>>>>>>>>>>>>>>>>>>>>>      corresponds to
>>>>>>>>>>>>>>>>>>>>>      H maps ⟨Ĥ⟩ ⟨Ĥ⟩ to H.qy"
>>>>>>>>>>>>>>>>>>>>> and
>>>>>>>>>>>>>>>>>>>>>      "The copy of H at Ĥ.qx correctly decides that
>>>>>>>>>>>>>>>>>>>>> its input never halts.
>>>>>>>>>>>>>>>>>>>>>      H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ correctly decides that
>>>>>>>>>>>>>>>>>>>>> its input halts"
>>>>>>>>>>>>>>>>>>>>> so this has nothing to do with Linz.  He is talking
>>>>>>>>>>>>>>>>>>>>> about Turing
>>>>>>>>>>>>>>>>>>>>> machines.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> The Linz conclusion only pertains to the behavior
>>>>>>>>>>>>>>>>>>>> the copy of H
>>>>>>>>>>>>>>>>>>>> embedded within Ĥ applied to ⟨Ĥ⟩ ⟨Ĥ⟩.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Everything Linz says, everything, is predicated on
>>>>>>>>>>>>>>>>>>> what a Turing machine
>>>>>>>>>>>>>>>>>>> is.  Unlike Turing machines, your machines are magic
>>>>>>>>>>>>>>>>>>> -- identical state
>>>>>>>>>>>>>>>>>>> transition functions can entail different
>>>>>>>>>>>>>>>>>>> configuration sequences for
>>>>>>>>>>>>>>>>>>> the same input.  Nothing you say has any relevance to
>>>>>>>>>>>>>>>>>>> Linz's Turing
>>>>>>>>>>>>>>>>>>> machines until you categorically repudiate this
>>>>>>>>>>>>>>>>>>> nonsense.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> That your only rebuttal to what I say now is dredging
>>>>>>>>>>>>>>>>>> up what I said
>>>>>>>>>>>>>>>>>> many months ago proves that you are being dishonest.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> You said this:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>    "The copy of H at Ĥ.qx correctly decides that its
>>>>>>>>>>>>>>>>> input never halts.
>>>>>>>>>>>>>>>>>    H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ correctly decides that its
>>>>>>>>>>>>>>>>> input halts"
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> If ⟨H⟩ and ⟨Ĥ⟩ were identical finite strings then they
>>>>>>>>>>>>>>>> must derive the same result. They are not identical
>>>>>>>>>>>>>>>> final strings.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> four days ago and you haven't retracted it.  Until you
>>>>>>>>>>>>>>>>> do, when you
>>>>>>>>>>>>>>>>> write Ĥ your readers must assume that you are referring
>>>>>>>>>>>>>>>>> to something
>>>>>>>>>>>>>>>>> about which this quote applies.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> What's more, for your remarks to have any bearing on
>>>>>>>>>>>>>>>>> Linz's Ĥ you must
>>>>>>>>>>>>>>>>> not only repudiate what you said, you must accept the
>>>>>>>>>>>>>>>>> converse,
>>>>>>>>>>>>>>>>> i.e. that if
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>    Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊦* Ĥ.qn
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> then
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>    H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊦* H.qn
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> So, do you retract what you said and accept this fact
>>>>>>>>>>>>>>>>> about Linz's H and
>>>>>>>>>>>>>>>>> Ĥ?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> You you continue to say that you believe that a decider
>>>>>>>>>>>>>>>> must report on its own behavior when you already know
>>>>>>>>>>>>>>>> damn well that a decider only computes the mapping from
>>>>>>>>>>>>>>>> its inputs to its own final state.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> A Decider must report on its own behavior (or the
>>>>>>>>>>>>>>> behavior of a copy of it) if that is what the input asks
>>>>>>>>>>>>>>> for.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You know that a decider only computes the mapping from its
>>>>>>>>>>>>>> input finite strings to its own final state thus you know
>>>>>>>>>>>>>> that you lie what you say that a decider must compute the
>>>>>>>>>>>>>> mapping from a non-finite sting non-input.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> WHY LIE ?  WHY LIE ?  WHY LIE ?  WHY LIE ?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> I don't, but you seem to like to.
>>>>>>>>>>>>>
>>>>>>>>>>>>> I never said that H needs to compute a mapping of anything
>>>>>>>>>>>>> but what has been given as an input.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The only thing H needs to compute the mapping of is <H^>
>>>>>>>>>>>>> <H^>, which is EXACTLY the string on its input.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The problem which you don't seem to understand is that the
>>>>>>>>>>>>> MAPPING it needs to try and compute (and which is not
>>>>>>>>>>>>> guaranteed to BE Computable), is the Behavior of the
>>>>>>>>>>>>> machine it represents, H^ applied to <H^>, as that is the
>>>>>>>>>>>>> mapping of the Halting Function.
>>>>>>>>>>>>
>>>>>>>>>>>> That is a non finite string non input, so you lied.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> <H^> <H^> is a finite string, which is what needs to be
>>>>>>>>>>> mapped, so you are just lying.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> On 3/23/2022 6:04 PM, Richard Damon wrote:
>>>>>>>>>>  > the MAPPING it needs to try and compute (and which is
>>>>>>>>>>  > not guaranteed to BE Computable), is the Behavior of
>>>>>>>>>>  > the machine it represents, H^ applied to <H^>,
>>>>>>>>>>
>>>>>>>>>> So you are just bald faced liar then.
>>>>>>>>>> It does not map H^ applied to <H^> to anything.
>>>>>>>>>> It maps ⟨Ĥ⟩ ⟨Ĥ⟩ to Ĥ.qn
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I never said it did.
>>>>>>>>>
>>>>>>>>> It maps the INPUT: <H^> <H^> to (OUTPUT) Qy or Qn based on (THE
>>>>>>>>> FUNCTION) whether H^ applied to <H^> will Halt.
>>>>>>>>
>>>>>>>> It must map the input to an accept or reject state based on the
>>>>>>>> actual behavior actually specified by this input as measured by
>>>>>>>> N steps of the correct UTM simulation of this input.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> Almost, it must map the INPUT <H^> <H^> to an OUTPUT Qy or Qn,
>>>>>>> based on the FUNCTION it is computing.
>>>>>>>
>>>>>>> There is NO requirement that it be based on its on simulation, or
>>>>>>> only N steps of a UTM.
>>>>>>>
>>>>>>
>>>>>> None-the-less if the behavior that is being measured is not
>>>>>> exactly the same behavior as the UTM simulation of the input then
>>>>>> the behavior being measured is measured incorrectly.
>>>>>>
>>>>>> A finite number of N steps is a mandatory constraint otherwise it
>>>>>> would be OK to report that infinite execution never halts after an
>>>>>> infinite number of steps.
>>>>>>
>>>>>
>>>>> You logic is backwards. You are just showing why it CAN'T be done,
>>>>> not why it must not be defined that way.
>>>>>
>>>>> The behavior that is measured MUST be exactly the behavior of the
>>>>> UTM simulation,
>>>>
>>>> In other words your requirement for a halt decider is that it
>>>> sometimes never halts.
>>>>
>>>
>>> Again, you are mixing REQUIREMENTS and CAPABILITIES.
>>>
>>> All deciders MUST Halt in finite time.
>>
>> And all deciders that simulate their infinitely repeating input are
>> not allowed to ever stop.
>>
>> If they recognize an infinitely repeating pattern in N steps of
>> simulation they are not allowed to report this otherwise the
>> simulation is not accurate.
>>
>>
>
> No, if they can CORRECTLY prove that their input will NEVER halt (even
> if they abort their simulation of them and go to Qn)

If you honestly believe that when a simulated input has been aborted
that this aborted simulated input continues to execute until it reaches
its own final state you are a clueless wonder.

When embedded_H determines that its simulated input cannot possibly
reach its final state it aborts the first simulated element which causes
the entire simulated chain to immediately stop.

--
Copyright 2021 Pete Olcott

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

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o Refuting the Peter Linz Halting Problem Proof V5 [ without an

By: olcott on Tue, 22 Mar 2022

31olcott
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