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computers / comp.ai.philosophy / Concise refutation of halting problem proofs V10 [ all rebuttals are categorically denied ]

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* Concise refutation of halting problem proofs V10 [ all rebuttals are categoricalolcott
`- Re: Concise refutation of halting problem proofs V10 [ fake rebuttalsolcott

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Concise refutation of halting problem proofs V10 [ all rebuttals are categorically denied ]

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Subject: Concise refutation of halting problem proofs V10 [ all rebuttals are categorically denied ]
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 by: olcott - Fri, 12 Nov 2021 20:11 UTC

#include <stdint.h>
typedef void (*ptr)();

int H(ptr x, ptr y)
{ x(y);
return 1;
}

// Minimal essence of Linz(1990) Ĥ
// and Strachey(1965) P (see below)
void P(ptr x)
{ H(x, x);
}

int main(void)
{ H(P, P);
}

It is obvious that the direct execution of the above code never halts
because it is infinitely recursive. It is equally obvious that when H
performs a correct pure simulation of its input (instead of directly
executing it) that its input never halts.

_P()
[00001a5e](01) 55 push ebp
[00001a5f](02) 8bec mov ebp,esp
[00001a61](03) 8b4508 mov eax,[ebp+08]
[00001a64](01) 50 push eax // push P
[00001a65](03) 8b4d08 mov ecx,[ebp+08]
[00001a68](01) 51 push ecx // push P
[00001a69](05) e810000000 call 00001a7e // call H
[00001a6e](03) 83c408 add esp,+08
[00001a71](01) 5d pop ebp
[00001a72](01) c3 ret
Size in bytes:(0021) [00001a72]

Because there is nothing that H can possibly do to cause or enable P to
reach its final state at 1a72 we correctly conclude that the input to
H(P,P) never halts.

For every possible H in the universe that is invoked at machine address
00001a7e the specific byte sequence of the machine code for P as input
to H(P,P) never halts. Thus all rebuttals in the universe are
categorically denied.

Halting problem undecidability and infinitely nested simulation (V2)
https://www.researchgate.net/publication/356105750_Halting_problem_undecidability_and_infinitely_nested_simulation_V2

--
Copyright 2021 Pete Olcott

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

Re: Concise refutation of halting problem proofs V10 [ fake rebuttals ]

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Subject: Re: Concise refutation of halting problem proofs V10 [ fake rebuttals
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 by: olcott - Fri, 12 Nov 2021 23:43 UTC

On 11/12/2021 5:13 PM, Richard Damon wrote:
> On 11/12/21 5:53 PM, olcott wrote:
>> On 11/12/2021 4:36 PM, Richard Damon wrote:
>>> On 11/12/21 5:24 PM, olcott wrote:
>>>> On 11/12/2021 4:13 PM, Richard Damon wrote:
>>>>> On 11/12/21 5:07 PM, olcott wrote:
>>>>>> On 11/12/2021 4:00 PM, Richard Damon wrote:
>>>>>>> On 11/12/21 3:11 PM, olcott wrote:
>>>>>>>> #include <stdint.h>
>>>>>>>> typedef void (*ptr)();
>>>>>>>>
>>>>>>>> int H(ptr x, ptr y)
>>>>>>>> {
>>>>>>>>    x(y);
>>>>>>>>    return 1;
>>>>>>>> }
>>>>>>>>
>>>>>>>> // Minimal essence of Linz(1990) Ĥ
>>>>>>>> // and Strachey(1965) P (see below)
>>>>>>>> void P(ptr x)
>>>>>>>> {
>>>>>>>>    H(x, x);
>>>>>>>> }
>>>>>>>>
>>>>>>>> int main(void)
>>>>>>>> {
>>>>>>>>    H(P, P);
>>>>>>>> }
>>>>>>>>
>>>>>>>> It is obvious that the direct execution of the above code never
>>>>>>>> halts because it is infinitely recursive. It is equally obvious
>>>>>>>> that when H performs a correct pure simulation of its input
>>>>>>>> (instead of directly executing it) that its input never halts.
>>>>>>>>
>>>>>>>> _P()
>>>>>>>> [00001a5e](01)  55              push ebp
>>>>>>>> [00001a5f](02)  8bec            mov ebp,esp
>>>>>>>> [00001a61](03)  8b4508          mov eax,[ebp+08]
>>>>>>>> [00001a64](01)  50              push eax        // push P
>>>>>>>> [00001a65](03)  8b4d08          mov ecx,[ebp+08]
>>>>>>>> [00001a68](01)  51              push ecx        // push P
>>>>>>>> [00001a69](05)  e810000000      call 00001a7e   // call H
>>>>>>>> [00001a6e](03)  83c408          add esp,+08
>>>>>>>> [00001a71](01)  5d              pop ebp
>>>>>>>> [00001a72](01)  c3              ret
>>>>>>>> Size in bytes:(0021) [00001a72]
>>>>>>>>
>>>>>>>> Because there is nothing that H can possibly do to cause or
>>>>>>>> enable P to reach its final state at 1a72 we correctly conclude
>>>>>>>> that the input to H(P,P) never halts.
>>>>>>>
>>>>>>> Wrong. IF H does abort and return 0 then the ACTUAL running of P
>>>>>>> will reach that address, and the actual running of P is what
>>>>>>> matters.
>>>>>>>
>>>>>>> All you have shown is that it is impossible for H to PROVE that P
>>>>>>> will be halting, not that P isn't Halting.
>>>>>>>
>>>>>> I have shown that P always specifies infinite recursion whether or
>>>>>> not this infinite recursion is aborted, therefore H(P,P)==0 is
>>>>>> always correct.
>>>>>
>>>>> No, you haven't.
>>>>>
>>>>> You logic makes the unsound step of FIRST assuming that H never
>>>>> aborts its operation, and THEN has H do an abort.
>>>>>
>>>>> If you DO have a valid proof that P(P) is non-halting when H(P,P)
>>>>> return 0 then you have just proved you logic system to be
>>>>> inconsistent as it can also be proved the if H(P,P) returns 0, that
>>>>> P(P) halts.
>>>>>
>>>>> A system that can prove a statement and its complement is
>>>>> inconsestent, and logically worthless.
>>>>>
>>>>>>
>>>>>> All rebuttals must take this form:
>>>>>> Find an invocation of H(P,P) at machine address 00001a7e such that
>>>>>> the simulation or execution of (the exact byte sequence of) P
>>>>>> reaches its final address of 00001a72.
>>>>>>
>>>>>> If no rebuttals exist this conclusively proves that H(P,P)==0 for
>>>>>> every H in the unverse.
>>>>>>
>>>>>
>>>>> WRONG CRITERIA.
>>>>>
>>>>> Just proves you are looking at POOP.
>>>>>
>>>>> The REAL halting problems asks what P(P) actually does.
>>>>>
>>>>
>>>> I proven beyond all possible doubt that the real P is infinitely
>>>> recursive in my latest example where H directly executes its input
>>>
>>>
>>> Yes, *IF* H just directly executes its input, then P(P) will be
>>> non-Halting,
>>
>> The ultimate measure of the halt status of an input is its behavior
>> when directly executed.
>>
>>> but H(P,P) never returns 0, so it is not a counter example.
>>>
>>
>> The fact that for every possible H that can possibly exist at at
>> machine address 00001a7e the simulation or execution of (the exact
>> byte sequence of) P never reaches its final address of 00001a72
>> conclusively proves that the input to H(P,P) never halts.
>>
>> The input to H(P,P) never halts therefore when H returns 0 it is
>> always correct.
>
> No, you have a fundamental error in your logic,
>
> FIRST, as has been explained before, but you just ignorantly ignore,
> 'inputs' do not have behavior, and as such do not halt or be
> non-halting. Halting is a property of COMPUTATIONS, not inputs. Thus
> your statement is proved conclusively FALSE because it makes an error in
> category (Maybe you don't understand these terms, but repeatedly
> ignoring them doesn't help your cause).

Because the simulated or executed input to every H(P,P) invoked at
machine address 00001a7e with the byte sequence of the machine code of P
as its input never reaches the final address of P at 00001a72 it is
always correct for this H(P,P) to return 0.

All rebuttals must take this form:
Find an invocation of H(P,P) at machine address 00001a7e such that the
simulation or execution of (the exact byte sequence of) P reaches its
final address of 00001a72.

Now that I have finally made my claim 100% perfectly precise when any
fake "rebuttal" side steps this claim with the strawman error (dishonest
dodge) it is very easy to tell.

--
Copyright 2021 Pete Olcott

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

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