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Aug 12, 2022, 1:41:29 PMAug 12

to

In message: <k9adnWtx-dZH62v_...@giganews.com>, on 12 of

August 2022,

Peter Olcott has admitted that his H does not satisfy:

H(X,Y)==0 if and only if X(Y) does not halt

so his H is NOT AN HALT DECIDER. PERIOD.

August 2022,

Peter Olcott has admitted that his H does not satisfy:

H(X,Y)==0 if and only if X(Y) does not halt

so his H is NOT AN HALT DECIDER. PERIOD.

Aug 12, 2022, 2:28:30 PMAug 12

to

that this simulation would never stop unless aborted.

typedef void (*ptr)();

int H(ptr p, ptr i); // simulating halt decider

void P(ptr x)

{

int Halt_Status = H(x, x);

if (Halt_Status)

HERE: goto HERE;

return;

}

int main()

{

Output("Input_Halts = ", H(P, P));

}

(1) I believe that most computer scientists would agree that a halt

decider must compute the mapping from its inputs to an accept or reject

state on the basis of the actual behavior specified by this input.

(2) Furthermore ALL computer scientists would agree that the correct

simulation of a machine description does derive the correct behavior

specified by this machine description.

This logically entails that when H(P,P) simulates its input until the

behavior of this input essentially matches the infinite recursion

behavior pattern, then H has correctly determined the halt status of P.

(a) The invoked H(P,P) simulates P(P) that calls a simulated H(P,P)

(b) that simulates P(P) that calls a simulated H(P,P)

(c) that simulates P(P) that calls a simulated H(P,P)...

Until H aborts the simulation of its input

I have "admitted" that (1) & (2) logically entails that H(P,P)==0 is

correct and if (1) & (2) is true then this proves that the assertion

that H(P,P) must be based on the behavior of P(P) is incorrect.

In other words the textbook definition of the halting function is proven

to be incorrect on the basis that it contradicts (1) & (2).

*Halting problem proofs refuted on the basis of software engineering* ?

https://www.researchgate.net/publication/361701808_Halting_problem_proofs_refuted_on_the_basis_of_software_engineering

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

Aug 12, 2022, 3:47:06 PMAug 12

to

so it's good it's back out in the open, but it's not really news.

In fact almost everything he has done since the manic post in Dec 2018

when he claimed to have "two actual Turing machines", H and H^, "exactly

and precisely as in Linz" "fully encoded" has been to find a way to

un-say this without it sounding too obviously wrong.

For a while, there was a patch of comparatively clear post-hoc

justification going on: H(P,P) == 0 is correct even though P(P) halts

because ... (insert your favourite of several reason here)[1] but that

was way too clear.

[1] Mine is "because P(P) would not halt if line 15 of H were commented

out"!

--

Ben.

Aug 12, 2022, 3:48:08 PMAug 12

to

Aug 12, 2022, 4:00:07 PMAug 12

to

A simulating halt decider simulates its input until it correctly proves

that this simulation would never stop unless aborted.

typedef void (*ptr)();

int H(ptr p, ptr i); // simulating halt decider

void P(ptr x)

{

int Halt_Status = H(x, x);

if (Halt_Status)

HERE: goto HERE;

return;

}

int main()

{

Output("Input_Halts = ", H(P, P));

}

The only way to show that the halting function is defined correctly is
that this simulation would never stop unless aborted.

typedef void (*ptr)();

int H(ptr p, ptr i); // simulating halt decider

void P(ptr x)

{

int Halt_Status = H(x, x);

if (Halt_Status)

HERE: goto HERE;

return;

}

int main()

{

Output("Input_Halts = ", H(P, P));

}

to find an error in (1) or (2).

(1) I believe that most computer scientists would agree that a halt

decider must compute the mapping from its inputs to an accept or reject

state on the basis of the actual behavior specified by this input.

(2) Furthermore ALL computer scientists would agree that the correct

simulation of a machine description does derive the correct behavior

specified by this machine description.

This logically entails that when H(P,P) simulates its input until the

behavior of this input essentially matches the infinite recursion

behavior pattern, then H has correctly determined the halt status of P.

halting function requiring H(P,P) to base its halt status decision on

the behavior of non-input P(P) is incorrect.

*Finding an error in (1) or (2) is the only way to*

*show that the halting function is defined correctly*

*Finding an error in (1) or (2) is the only way to*

*show that the halting function is defined correctly*

*Finding an error in (1) or (2) is the only way to*

*show that the halting function is defined correctly*

Aug 12, 2022, 4:01:43 PMAug 12

to

one of them can be correct.

*Finding an error in (1) or (2) is the only way to*

*show that the halting function is defined correctly*

*Finding an error in (1) or (2) is the only way to*

*show that the halting function is defined correctly*

*Finding an error in (1) or (2) is the only way to*

*show that the halting function is defined correctly*

Aug 12, 2022, 4:11:06 PMAug 12

to

On Friday, August 12, 2022 at 11:28:30 AM UTC-7, olcott wrote:

>

> (1) I believe that most computer scientists would agree that a halt

> decider must compute the mapping from its inputs to an accept or reject

> state on the basis of the actual behavior specified by this input.

>

This is the definition of halt decider.
>

> (1) I believe that most computer scientists would agree that a halt

> decider must compute the mapping from its inputs to an accept or reject

> state on the basis of the actual behavior specified by this input.

>

>

> (2) Furthermore ALL computer scientists would agree that the correct

> simulation of a machine description does derive the correct behavior

> specified by this machine description.

>

This is the definition of simulation
> (2) Furthermore ALL computer scientists would agree that the correct

> simulation of a machine description does derive the correct behavior

> specified by this machine description.

>

>

> This logically entails that when H(P,P) simulates its input until the

> behavior of this input essentially matches the infinite recursion

> behavior pattern, then H has correctly determined the halt status of P.

>

This does not follow. Not all non-halting simulations ever show that
> This logically entails that when H(P,P) simulates its input until the

> behavior of this input essentially matches the infinite recursion

> behavior pattern, then H has correctly determined the halt status of P.

>

pattern.

Aug 12, 2022, 4:19:36 PMAug 12

to

On 8/12/2022 3:09 PM, dklei...@gmail.com wrote:

> On Friday, August 12, 2022 at 11:28:30 AM UTC-7, olcott wrote:

>>

>> (1) I believe that most computer scientists would agree that a halt

>> decider must compute the mapping from its inputs to an accept or reject

>> state on the basis of the actual behavior specified by this input.

>>

> This is the definition of halt decider.

Yes it is. In order to begin to show otherwise requires more than a
> On Friday, August 12, 2022 at 11:28:30 AM UTC-7, olcott wrote:

>>

>> (1) I believe that most computer scientists would agree that a halt

>> decider must compute the mapping from its inputs to an accept or reject

>> state on the basis of the actual behavior specified by this input.

>>

> This is the definition of halt decider.

dogmatic statement that you believe it is incorrect, it requires

pointing out the exact error and all of the reasoning why it is an error.

>>

>> (2) Furthermore ALL computer scientists would agree that the correct

>> simulation of a machine description does derive the correct behavior

>> specified by this machine description.

>>

> This is the definition of simulation

>>

>> This logically entails that when H(P,P) simulates its input until the

>> behavior of this input essentially matches the infinite recursion

>> behavior pattern, then H has correctly determined the halt status of P.

>>

> This does not follow. Not all non-halting simulations ever show that

> pattern.

>

Aug 12, 2022, 4:26:16 PMAug 12

to

For *any* algorithm X and input Y:

H(X,Y)==1 if and only if X(Y) halts, and

H(X,Y)==0 if and only if X(Y) does not halt

And it directly follows from this that "the actual behavior specified by this input" is defined to be the behavior of X(Y), not the behavior of some simulator.
In the case of Ha(Pa,Pa), this means "the actual behavior specified by this input" is the behavior of Pa(Pa), not the behavior of Pn(Pn) as you like to claim:

On Saturday, July 30, 2022 at 4:09:34 PM UTC-4, olcott wrote:

> H(P,P) is asking would the input that I correctly emulate ever reach its

> "ret" instruction (final state) if I never stopped emulating it?

On Wednesday, August 10, 2022 at 6:11:10 PM UTC-4, olcott wrote:

> This is the correct point in the execution trace to put the simulator:

>

> void P(ptr x)

> {

> int Halt_Status = Simulate(x, x);

> if (Halt_Status)

> HERE: goto HERE;

> return;

> }

>

> HERE: goto HERE;

> return;

> }

>

> (2) Furthermore ALL computer scientists would agree that the correct

> simulation of a machine description does derive the correct behavior

> specified by this machine description.

FALSE. It would be the correct AND COMPLETE simulation, not some simulation that was aborted. Counterexample: Ha3(N,5) does a correct but not complete simulation, and it is obvious that Ha3(N,5)==0 is wrong because N(5) aborts.
> simulation of a machine description does derive the correct behavior

> specified by this machine description.

>

> This logically entails that when H(P,P) simulates its input until the

> behavior of this input essentially matches the infinite recursion

> behavior pattern, then H has correctly determined the halt status of P.

Aug 12, 2022, 5:55:13 PMAug 12

to

On 8/12/22 2:28 PM, olcott wrote:

> On 8/12/2022 12:41 PM, Python wrote:

>> In message: <k9adnWtx-dZH62v_...@giganews.com>, on 12 of

>> August 2022,

>>

>> Peter Olcott has admitted that his H does not satisfy:

>>

>> H(X,Y)==0 if and only if X(Y) does not halt

>>

>> so his H is NOT AN HALT DECIDER. PERIOD.

>>

>>

>

> A simulating halt decider simulates its input until it correctly proves

> that this simulation would never stop unless aborted.

>

So why does yours stop before it does that?
> On 8/12/2022 12:41 PM, Python wrote:

>> In message: <k9adnWtx-dZH62v_...@giganews.com>, on 12 of

>> August 2022,

>>

>> Peter Olcott has admitted that his H does not satisfy:

>>

>> H(X,Y)==0 if and only if X(Y) does not halt

>>

>> so his H is NOT AN HALT DECIDER. PERIOD.

>>

>>

>

> A simulating halt decider simulates its input until it correctly proves

> that this simulation would never stop unless aborted.

>

Because it uses UNSOUND logic and thus is wrong.

> typedef void (*ptr)();

> int H(ptr p, ptr i); // simulating halt decider

>

> void P(ptr x)

> {

> int Halt_Status = H(x, x);

> if (Halt_Status)

> HERE: goto HERE;

> return;

> }

>

> int main()

> {

> Output("Input_Halts = ", H(P, P));

> }

>

> (1) I believe that most computer scientists would agree that a halt

> decider must compute the mapping from its inputs to an accept or reject

> state on the basis of the actual behavior specified by this input.

>

> (2) Furthermore ALL computer scientists would agree that the correct

> simulation of a machine description does derive the correct behavior

> specified by this machine description.

>

> This logically entails that when H(P,P) simulates its input until the

> behavior of this input essentially matches the infinite recursion

> behavior pattern, then H has correctly determined the halt status of P.

>

> (a) The invoked H(P,P) simulates P(P) that calls a simulated H(P,P)

> (b) that simulates P(P) that calls a simulated H(P,P)

> (c) that simulates P(P) that calls a simulated H(P,P)...

> Until H aborts the simulation of its input

>

> I have "admitted" that (1) & (2) logically entails that H(P,P)==0 is

> correct and if (1) & (2) is true then this proves that the assertion

> that H(P,P) must be based on the behavior of P(P) is incorrect.

of the input.

>

> In other words the textbook definition of the halting function is proven

> to be incorrect on the basis that it contradicts (1) & (2).

but incorrect presume the behavior of H, so you get the wrong answer.

Aug 13, 2022, 12:28:43 AMAug 13

to

On Friday, August 12, 2022 at 1:19:36 PM UTC-7, olcott wrote:

> On 8/12/2022 3:09 PM, dklei...@gmail.com wrote:

> > On Friday, August 12, 2022 at 11:28:30 AM UTC-7, olcott wrote:

> >>

> >> (1) I believe that most computer scientists would agree that a halt

> >> decider must compute the mapping from its inputs to an accept or reject

> >> state on the basis of the actual behavior specified by this input.

> >>

> > This is the definition of halt decider.

> Yes it is. In order to begin to show otherwise requires more than a

> dogmatic statement that you believe it is incorrect, it requires

> pointing out the exact error and all of the reasoning why it is an error.

> >>

> >> (2) Furthermore ALL computer scientists would agree that the correct

> >> simulation of a machine description does derive the correct behavior

> >> specified by this machine description.

> >>

> > This is the definition of simulation

> >>

> >> This logically entails that when H(P,P) simulates its input until the

> >> behavior of this input essentially matches the infinite recursion

> >> behavior pattern, then H has correctly determined the halt status of P.

> >>

> > This does not follow. Not all non-halting simulations ever show that

> > pattern.

> >

> So you did not bother to notice that I am talking about a specific H/P ?

You did not say that was the case.
> On 8/12/2022 3:09 PM, dklei...@gmail.com wrote:

> > On Friday, August 12, 2022 at 11:28:30 AM UTC-7, olcott wrote:

> >>

> >> (1) I believe that most computer scientists would agree that a halt

> >> decider must compute the mapping from its inputs to an accept or reject

> >> state on the basis of the actual behavior specified by this input.

> >>

> > This is the definition of halt decider.

> Yes it is. In order to begin to show otherwise requires more than a

> dogmatic statement that you believe it is incorrect, it requires

> pointing out the exact error and all of the reasoning why it is an error.

> >>

> >> (2) Furthermore ALL computer scientists would agree that the correct

> >> simulation of a machine description does derive the correct behavior

> >> specified by this machine description.

> >>

> > This is the definition of simulation

> >>

> >> This logically entails that when H(P,P) simulates its input until the

> >> behavior of this input essentially matches the infinite recursion

> >> behavior pattern, then H has correctly determined the halt status of P.

> >>

> > This does not follow. Not all non-halting simulations ever show that

> > pattern.

> >

> So you did not bother to notice that I am talking about a specific H/P ?

What specific H and P do your comments assume and how do they relate

to (1) and (2) above?

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