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 H of H(P,P) where P(P) calls this same H(P,P) and H simulates
or executes its input and aborts or does not abort its input.
[PSR_set] ∀{H,P} ∊ PSR_set (Input_Never_Halts( H(P,P) ))
[PSR_subset_A] ∃{H,P} ∊ PSR_set (Halts( H(P,P) ))
[PSR_subset_B] ∃{H,P} ∊ PSR_set (Halts( P(P) ))
[PSR_subset_C] The subset of the PSR_subset_A where H returns 0 on the
basis that H correctly detects that its input never halts (reaches its
final instruction). H could detect that its simulated P is calling
H(P,P) with the same parameters that it was called with, thus specifying infinite recursion.
H is a computable function that accepts or rejects inputs in its domain
on the basis that these inputs specify a sequence of configurations that
reach their final state.
H is a correct decider and H has a correct halt deciding basis.
*(see page 3)*
Halting problem undecidability and infinitely nested simulation V2
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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