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

#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);
}

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
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.

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
subset the input to H(P,P) never halts and H(P,P) halts.

When int main(void) { P(P); } is invoked on H/P elements of the above
PSR subset, then we have a cases where the input to H(P,P) never halts
and P(P) halts.

This conclusively proves when the input to H(P,P) never halts and the
same P(P) does halt that this does not form a contradiction.



Halting problem undecidability and infinitely nested simulation (V2)
November 2021 PL Olcott

https://www.researchgate.net/publication/356105750_Halting_problem_undecidability_and_infinitely_nested_simulation_V2


--
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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