Concise refutation of halting problem proofs V25 [ H is a computable fu
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olcott@21:1/5 to
All on Sun Nov 21 18:03:52 2021
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
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.
[PSR subset + P(P) set] Appending the computation int main(void) { P(P);
} to the PSR subset on the basis of the exact same H/P pairs that are in
this subset we find that this P(P) halts while the input to its
corresponding H(P,P) never halts.
[Decidable_PSR subset] The subset of the PSR subset where H returns 0 on
the basis that H correctly detects that P specifies infinite recursion
defines the decidable domain of function H.
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.
The above 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.
--
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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