void Px(ptr x)
{
int Halt_Status = Hx(x, x);
if (Halt_Status)
HERE: goto HERE;
return;
}
int main()
{
Output("Input_Halts = ", Hx(Px, Px));
}
*Understanding the above code proves this*
There are zero elements of infinite set of Hx/Px pairs such that the
correct *partial or complete* simulation of Px by Hx reaches the final
state of Px.
*THIS LOGICALLY FOLLOWS (as a subset) FROM ABOVE*
(A) Every element of the infinite set of Hx/Px pairs that does a correct
and complete simulation of its input never reaches the final state of
this input.
*THIS IS THE DEFINITION OF A UTM THUS KNOWN TO BE TRUE*
(B) A correct and complete simulation of Px by Hx derives the actual
behavior of Px.
*THIS LOGICALLY FOLLOWS FROM (A) AND (B) PREMISES*
(C) The actual behavior of this input never reaches the final state of
this input.
When the criteria for a simulating halt decider (SHD) is to correctly
predict that its complete and correct simulation of its input would
never reach the final state of this simulated input then:
void Infinite_Loop()
{
HERE: goto HERE;
}
*H0(Infinite_Loop)==0 // is correct*
void Infinite_Recursion(int N)
{
Infinite_Recursion(N);
}
*H(Infinite_Recursion, 0x777)==0 // is correct*
Every Hx that returns zero correctly predicts that every Px correctly
and completely simulated by any Hx never reaches the final state of Px.
*Hx(Px,Px)==0 // is correct*
computation that halts … the Turing machine will halt whenever it enters
a final state. (Linz:1990:234)
The particular instance of Hx named H and contained in Halt7.c does
correctly predict
that the arguments to H(P,P) cannot possibly reach their own final
state. H makes this
prediction on the basis of correctly matching a correct
infinite-behavior pattern.
*complete halt deciding system including*
*(a) x86utm operating system*
*(b) complete x86 emulator*
*(c) All of the various halt deciders and their inputs are contained in
Halt7.c*
https://liarparadox.org/2022_09_07.zip
This system currently only compiles under:
Microsoft Visual Studio Community 2017
https://visualstudio.microsoft.com/vs/older-downloads/
*Halting problem proofs refuted on the basis of software engineering* ?
https://www.researchgate.net/publication/361701808_Halting_problem_proofs_refuted_on_the_basis_of_software_engineering
Linz, Peter 1990. An Introduction to Formal Languages and Automata.
Lexington/Toronto: D. C. Heath and Company. (317-320)
--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer