XPost: comp.theory, sci.logic, sci.math
On 11/22/2021 10:05 AM, Richard Damon wrote:
On 11/22/21 10:28 AM, olcott wrote:
On 11/22/2021 6:20 AM, Python wrote:
olcott wrote:
#include <stdint.h>
#include <stdio.h>
typedef int (*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);
}
$ ./olcott
Segmentation fault: 11
Thus proving that H(P,P) never halts.
And if H(P,P) never halts, it isn't a valid decider.
FAIL.
I take back that you are sufficiently technically competent to
comprehend any of the following, not even the Linz quote:
Computation that halts
a computation is said to halt whenever it enters a final state.
(Linz:1990:234)
[PSR set] Combinations of H/P having pathological self-reference
Every 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.
[PSR subset] Because we know that the input to H(P,P) never halts for
the whole PSR set and a subset of these H/P combinations aborts the
execution or simulation of its input then we know that for this entire
PSR subset the input to H(P,P) never halts and H(P,P) halts.
--
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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