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.

--
Copyright 2021 Pete Olcott

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