On 7/10/2021 11:34 AM, Mr Flibble wrote:
> On Sat, 10 Jul 2021 11:08:35 -0500
> olcott <NoOne@NoWhere.com> wrote:
>
>> On 7/10/2021 10:25 AM, Mr Flibble wrote:
>>> On Sat, 10 Jul 2021 10:21:26 -0500
>>> olcott <NoOne@NoWhere.com> wrote:
>>>
>>>> On 7/10/2021 10:15 AM, Mr Flibble wrote:
>>>>> On Sat, 10 Jul 2021 10:00:51 -0500
>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>
>>>>>> On 7/10/2021 9:30 AM, Mr Flibble wrote:
>>>>>>> On Sat, 10 Jul 2021 08:54:23 -0500
>>>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>>>
>>>>>>>> On 7/10/2021 6:40 AM, Mr Flibble wrote:
>>>>>>>>> On Fri, 9 Jul 2021 16:13:48 -0500
>>>>>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>>>>>
>>>>>>>>>> On 7/9/2021 4:08 PM, Mr Flibble wrote:
>>>>>>>>>>> On Fri, 9 Jul 2021 14:24:33 -0500
>>>>>>>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>>>>>>>
>>>>>>>>>>>> On 7/9/2021 2:16 PM, Mr Flibble wrote:
>>>>>>>>>>>>> On Fri, 9 Jul 2021 12:47:12 -0500
>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> On 7/9/2021 12:06 PM, Mr Flibble wrote:
>>>>>>>>>>>>>>> On Fri, 9 Jul 2021 08:59:51 -0500
>>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> wrote:
>>>>>>>>>>>>>>>> [Halt Deciding Axiom] When the pure simulation of the
>>>>>>>>>>>>>>>> machine description ⟨P⟩ of a machine P on its input I
>>>>>>>>>>>>>>>> never halts we know that P(I) never halts.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> No we cannot. In order to remove the pathological
>>>>>>>>>>>>>>>> feedback loop such that P does the opposite of whatever
>>>>>>>>>>>>>>>> H decides H simply acts as a pure simulator of P thus
>>>>>>>>>>>>>>>> having no effect what-so-ever on the behavior of P
>>>>>>>>>>>>>>>> until after its halt status decision has been made.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Except your decider can only handle trivial
>>>>>>>>>>>>>>> uninteresting cases: if you wish to make progress on
>>>>>>>>>>>>>>> this then prove your decider works with a non-trivial
>>>>>>>>>>>>>>> case which includes branching logic predicated on
>>>>>>>>>>>>>>> arbitrary program input that is unknown a priori to the
>>>>>>>>>>>>>>> simulation starting; but before you even do that prove
>>>>>>>>>>>>>>> your decider works with a non-trivial case with
>>>>>>>>>>>>>>> branching logic predicated on arbitrary program input
>>>>>>>>>>>>>>> that *is* known a priori.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You continue to prove to everyone that actually knows
>>>>>>>>>>>>>> these things that you are an ignoramus on this subject.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> That H correctly decides that all of the standard
>>>>>>>>>>>>>> counter-examples templates never halt eliminates the
>>>>>>>>>>>>>> entire basis of all of the conventional halting problem
>>>>>>>>>>>>>> undecidability proofs.
>>>>>>>>>>>>>>> I also note that you repeatedly refuse to address my
>>>>>>>>>>>>>>> point regarding how x86 mov instructions can read/write
>>>>>>>>>>>>>>> from/to memory mapped I/O rather than RAM so the result
>>>>>>>>>>>>>>> of the mov instruction cannot be known a priori. The
>>>>>>>>>>>>>>> halting program concerns computing devices and a
>>>>>>>>>>>>>>> computing device which cannot do I/O is next to
>>>>>>>>>>>>>>> useless, much like your decider (until you actually
>>>>>>>>>>>>>>> prove otherwise which I have a feeling is never going
>>>>>>>>>>>>>>> to happen as you appear to be stuck in a loop).
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> I continue to note that you repeatedly refuse to address
>>>>>>>>>>>>> my point regarding how x86 mov instructions can read/write
>>>>>>>>>>>>> from/to memory mapped I/O rather than RAM so the result of
>>>>>>>>>>>>> the mov instruction cannot be known a priori. The halting
>>>>>>>>>>>>> program concerns computing devices and a computing device
>>>>>>>>>>>>> which cannot do I/O is next to useless, much like your
>>>>>>>>>>>>> decider (until you actually prove otherwise which I have a
>>>>>>>>>>>>> feeling is never going to happen as you appear to be stuck
>>>>>>>>>>>>> in a loop).
>>>>>>>>>>>>>
>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> You are the only one that believes that your points have
>>>>>>>>>>>> any relevance. That you believe that data movement
>>>>>>>>>>>> instructions have anything to do with control flow proves
>>>>>>>>>>>> that your points have no relevance.
>>>>>>>>>>>
>>>>>>>>>>> You literally have no clue about what you are talking about,
>>>>>>>>>>> whatsoever. This explains everything.
>>>>>>>>>>>
>>>>>>>>>>> /Flibble
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> *Make sure that you read all of this especially the last
>>>>>>>>>> line*
>>>>>>>>>>
>>>>>>>>>> halt (p, i)
>>>>>>>>>> {
>>>>>>>>>> if ( program p halts on input i )
>>>>>>>>>> return true ; // p halts
>>>>>>>>>> else
>>>>>>>>>> return false ; // p doesn’t halt
>>>>>>>>>> }
>>>>>>>>>> Fig. 1. Pseudocode of the Halting Function
>>>>>>>>>>
>>>>>>>>>> Strachey’s Impossible Program Strachey proposed a program
>>>>>>>>>> based on the result of an assumed halting function [2].
>>>>>>>>>> The way Strachey’s construction and other similar
>>>>>>>>>> constructions are used to show the impossibility of a
>>>>>>>>>> decideable halting function is quite similar to Turing’s
>>>>>>>>>> original disproof. But the relevant difference we want to
>>>>>>>>>> emphasize is that they do not explicitly assume an infinite
>>>>>>>>>> number of possible machines (programs) or input data,
>>>>>>>>>> because they directly use reductio ad absurdum to prove that
>>>>>>>>>> both, Strachey’s construction and the universal halting
>>>>>>>>>> function cannot exist.
>>>>>>>>>>
>>>>>>>>>> strachey ( p )
>>>>>>>>>> {
>>>>>>>>>> if ( halt (p, p) == true )
>>>>>>>>>> L1 : goto L1 ; // loop forever
>>>>>>>>>> else
>>>>>>>>>> return;
>>>>>>>>>> }
>>>>>>>>>>
>>>>>>>>>> Fig. 2. Strachey’s Impossible Program
>>>>>>>>>>
>>>>>>>>>> The impossibility of Strachey’s construction given in Figure
>>>>>>>>>> 2 becomes obvious if one tries to apply the halting function
>>>>>>>>>> as follows:
>>>>>>>>>>
>>>>>>>>>> halt(strachey, strachey)
>>>>>>>>>>
>>>>>>>>>> Since in this case strachey() itself calls halt(strachey,
>>>>>>>>>> strachey), it is required that the direct call of halt() and
>>>>>>>>>> the nested call provide the same result. However, this leads
>>>>>>>>>> to a contradiction, whatever result halt() returns. Within
>>>>>>>>>> this disproof there seems to be no indication why not it
>>>>>>>>>> could be even applied to finite-state systems having a
>>>>>>>>>> concrete upper bound of state space.
>>>>>>>>>>
>>>>>>>>>> https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.206.1468&rep=rep1&type=pdf
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Except your decider can only handle trivial uninteresting
>>>>>>>>> cases: if you
>>>>>>>>
>>>>>>>> Ask other people here if being able to correctly decide the
>>>>>>>> strachey case is trivial or uninteresting. Ben might be the
>>>>>>>> best one to ask about this.
>>>>>>>>
>>>>>>>> Here is his original 1965 letter.
>>>>>>>> https://academic.oup.com/comjnl/article/7/4/313/354243
>>>>>>>
>>>>>>> All Strachey's letter shows is that a decider cannot be part of
>>>>>>> that which is being decided.
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>>
>>>>>> // Simplified Linz Ĥ (Linz:1990:319)
>>>>>> void P(u32 x)
>>>>>> {
>>>>>> u32 Input_Halts = H(x, x);
>>>>>> if (Input_Halts)
>>>>>> HERE: goto HERE;
>>>>>> }
>>>>>>
>>>>>> int main()
>>>>>> {
>>>>>> u32 Input_Halts = H((u32)P, (u32)P);
>>>>>> Output("Input_Halts = ", Input_Halts);
>>>>>> }
>>>>>>
>>>>>> What it shows is that the halting problem proof can be enormously
>>>>>> simplified to the impossibility of the H(P,P) in main()
>>>>>> returning a correct halt status value to main().
>>>>>>
>>>>>> *Here are Strachey's (verbatim) own words*
>>>>>> Suppose T[R] is a Boolean function taking a routine
>>>>>> (or program) R with no formal or free variables as its
>>>>>> argument and that for all R, T[R] — True if R terminates
>>>>>> if run and that T[R] = False if R does not terminate.
>>>>>> Consider the routine P defined as follows
>>>>>>
>>>>>> rec routine P
>>>>>> §L:if T[P] go to L
>>>>>> Return §
>>>>>>
>>>>>> If T[P] = True the routine P will loop, and it will
>>>>>> only terminate if T[P] = False. In each case T[P] has
>>>>>> exactly the wrong value, and this contradiction shows
>>>>>> that the function T cannot exist.
>>>>>>
>>>>>> Strachey is the creator of CPL ancestor to BCPL then B then C
>>>>>> His code above is written in his CPL programming language.
>>>>>
>>>>> I repeat: all Strachey's letter shows is that a decider cannot be
>>>>> part of that which is being decided.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> Although this <is> one way of putting it, all of the halting
>>>> problem proofs require that the decider is a part of what is being
>>>> decided. When we disallow that all of these proofs lose their
>>>> entire basis and fail to prove anything.
>>>
>>> I agree, if these proofs do require a decider to be part of that
>>> which is being decided then they are indeed invalid for the reason
>>> Strachey highlights in his letter.
>>>
>>> /Flibble
>>>
>>
>> I have been saying that they are invalid since 2004, now you are
>> agreeing with me on this.
>>
>> comp.theory Peter Olcott Sep 5, 2004, 11:21:57 AM
>> The Liar Paradox can be shown to be nothing more than
>> a incorrectly formed statement because of its pathological
>> self-reference. The Halting Problem can only exist because
>> of this same sort of pathological self-reference.
>> https://groups.google.com/g/comp.theory/c/RO9Z9eCabeE/m/Ka8-xS2rdEEJ
>>
>> Everyone else believes that they are valid and prove that the halting
>> problem is undecidable.
>
> They are not valid as [Strachey 1965] falsifies them (if what you say
> is correct) HOWEVER given that it doesn't follow that the halting
> problem itself is not undecidable just that those particular proofs are
> invalid.
>
> /Flibble
>

You can check around.
You and I are the only one's here that hold that view.
Ben, Kaz, and Mike would all disagree with you and I on this point.

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein