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.

--
Copyright 2021 Pete Olcott

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