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computers / comp.ai.philosophy / Re: Concise refutation of halting problem proofs V10 [ fake rebuttals ]

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

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Subject: Concise refutation of halting problem proofs V10 [ all rebuttals are categorically denied ]
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, sci.logic, sci.math
Date: Fri, 12 Nov 2021 20:11 UTC
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Subject: Concise refutation of halting problem proofs V10 [ all rebuttals are categorically denied ]
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#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


Subject: Re: Concise refutation of halting problem proofs V10 [ fake rebuttals ]
From: olcott
Newsgroups: comp.theory, sci.logic, sci.math, comp.ai.philosophy
Followup: comp.theory
Date: Fri, 12 Nov 2021 23:43 UTC
References: 1 2 3 4 5 6 7 8
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Subject: Re: Concise refutation of halting problem proofs V10 [ fake rebuttals
]
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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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