XPost: comp.theory, sci.logic, sci.math

On 6/7/2022 9:41 PM, Mike Terry wrote:

On 08/06/2022 01:42, Mr Flibble wrote:

Hi,

 From discussion with Olcott in comp.lang.c++ I have determined that
his so called refutation of the HP proofs is based around the
behaviour of his simulation-based decider, H:

void Q(u32 x)
{
          if (H(x, x))
            FUBAR();
          return;
}

int main()
{
          Output("Input_Halts = ", H((u32)Q, (u32)Q));
}

He asserts H(Q,Q)=0 based on a nested simulation being detected (i.e. Q
invoking H) irregardless of whether FUBAR halts or not.

If FUBAR halts H gives the wrong answer.

Since his H returns 0 (given), the H(x,x) in Q is always false, so FUBAR
is never executed. Instead, Q always just returns.  So H gives the wrong answer regardless of FUBAR.

Yes it's that simple.

He claims H(Q,Q)=0 as it gets stuck in a recursive (nested) simulation
however that wouldn't be the case for non-simulating decider for which
there would be no such recursion.

Well, PO is only trying to make a case for ONE scenario: HIS H (he
claims) giving the correct answer for its associated H_Hat (now called
Q), contrary to what the Linz proof requires.  The proof covers /any/ halting detector design, including a "simulating halt detector", so his problem isn't the choice to use simulation.

But given the simple observation that his H gives the WRONG answer, the

THAT IS A RIDICULOUSLY STUPID THING TO SAY BECAUSE:
1) Deciders(computer science) compute the mapping from their inputs to
an accept or reject state.

(2) The actual behavior of the actual input to H(P,P) is proven to never
halt.

(3) P(P) is not an input to H, thus out-of-scope for H.

int sum( x, int y)
{
return x + y;
}

Expecting H(P,P) to compute the halt status of P(P) is as ridiculously
stupid as expecting sum(3,4) to return the sum of 7 + 9.

The correct simulation of the input to H(P,P) that has pathological self-reference (Olcott 2004) actually factually has different halting
behavior than the execution of P(P) that does not have pathological self-reference (Olcott 2004).

reasons /why/ PO thinks he is refuting anything are kind of irrelevant. (Unless you think there are interesting technical points to be discussed
- I'd say anything like that ended years ago and now it's just
repetition. Or you're interested in PO's case from a medical/psychology perspective, but then this is the wrong group to cover that.)

In any case, as it happens, PO's H(Q,Q) DOESN'T get stuck in infinite recursion!  While the computation Q(Q) internally /does/ recursively simulate the Q(Q) computation, Q contains [inside H] break-out tests
which match and abort the simulation from the outside.  The result is
that only a couple of levels of recursive simulation actually occur (no /infinite/ recursive simulation).

Can we finally put this to bed and change the fucking topic?

I stopped responding to PO a long time ago, because I realised it
genuinely achieved /absolutely/ nothing.  PO is not capable of
understanding what people are saying to him, so all the tens of
thousands of posts may as well never have occured for all their effect.

(Then again, comp.theory isn't doing much else these days!  So no harm
done either.)  :)

Mike.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

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