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

On 11/18/2021 1:01 PM, André G. Isaak wrote:

On 2021-11-18 10:23, olcott wrote:

On 11/18/2021 10:55 AM, Ben Bacarisse wrote:

Mr Flibble <flibble@reddwarf.jmc> writes:

On Thu, 18 Nov 2021 06:29:26 -0500
Richard Damon <Richard@Damon-Family.org> wrote:

H(P,P) is supposed to say what P(P) will do.

No,

So what arguments does one pass to H to find out is P(P) halts?

This is the same code that you modified.

???

How is that a response?

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

int H(ptr x, ptr y)
{
x(y); // direct execution of P(P)
return 1;
}

// Minimal essence of Linz(1990) Ĥ
// and Strachey(1965) P
int P(ptr x)
{
H(x, x);
return 1; // Give P a last instruction at the "c" level
}

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

We can see the arguments passed to H prove that P never reaches its last instruction.

We have a computation, P(P), which you acknowledge halts.

We have a precisely defined set of sequences of x86 instructions as combinations of H/P such that the relationship between H and P is always pathological self-reference:

For every possible H of H(P,P) invoked from main() where P(P) calls this
same H(P,P) and H simulates or executes its input and aborts or does not
abort its input P never reaches its last instruction.

P(P) is not in this set thus a strawman error when used as a rebuttal to
the behavior of elements in the defined set.

We also have H which you claim to be a halt decider.

I haven't gotten to that point yet, first I prove that the "impossible"
input is decidable, then after this is accepted then I show the trivial
step required for H to make this correct halt status decision.

So let's say someone doesn't know whether P(P) halts. But they have your
halt decider H, and a halt decider should be able to answer this
question for them. That's what halt deciders are for, after all.

A simple bench check of the 21 lines of C code conclusively proves that
P never reaches its final instruction.

A more complex analysis proves that no element of the infinite
pathological self-reference set of H/P does P ever reach its final
instruction.

So what input do they give to H so that H will correctly tell them that
P(P) halts?

André

--
Copyright 2021 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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