XPost: comp.theory, sci.logic, sci.math
On 6/18/2022 7:52 AM, Richard Damon wrote:
On 6/18/22 8:32 AM, olcott wrote:
On 6/18/2022 7:24 AM, wij wrote:
On Saturday, 18 June 2022 at 20:07:56 UTC+8, olcott wrote:
On 6/18/2022 4:09 AM, Malcolm McLean wrote:
On Friday, 17 June 2022 at 12:29:37 UTC+1, olcott wrote:
When a simulating halt decider rejects all inputs as non-halting
whenever it correctly detects that its correct and complete
simulation
of its input would never reach the final state of this input then all >>>>>> [these] inputs (including pathological inputs) are decided correctly. >>>>>>
*computation that halts* … the Turing machine will halt whenever it >>>>>> enters a final state. (Linz:1990:234)
Linz, Peter 1990. An Introduction to Formal Languages and Automata. >>>>>> Lexington/Toronto: D. C. Heath and Company. (317-320)
#include <stdint.h>
typedef void (*ptr)();
void P(ptr x)
{
if (H(x, x))
HERE: goto HERE;
return;
}
int main()
{
Output("Input_Halts = ", H(P, P));
}
_P()
[00001352](01) 55 push ebp
[00001353](02) 8bec mov ebp,esp
[00001355](03) 8b4508 mov eax,[ebp+08]
[00001358](01) 50 push eax // push P
[00001359](03) 8b4d08 mov ecx,[ebp+08]
[0000135c](01) 51 push ecx // push P
[0000135d](05) e840feffff call 000011a2 // call H
[00001362](03) 83c408 add esp,+08
[00001365](02) 85c0 test eax,eax
[00001367](02) 7402 jz 0000136b
[00001369](02) ebfe jmp 00001369
[0000136b](01) 5d pop ebp
[0000136c](01) c3 ret
Size in bytes:(0027) [0000136c]
(1) It is an easily verified fact that when we assume that H is
only an
x86 emulator that the correctly emulated P never reaches its "ret" >>>>>> instruction it remains stuck in repeated cycles of emulation.
Yes.
(2) It is an easily verified fact that if H has been adapted to
correctly detect (in a finite number of steps) that the correct and >>>>>> complete x86 emulation of its input would never each its "ret"
instruction that H could abort its emulation and return 0 to
report this.
Yes.
(3) When the halt status criteria is defined as correctly determining >>>>>> whether or not an x86 emulated input would ever reach its "ret"
instruction then it becomes an easily verified fact H(P,P) could
correctly reject its input as non-halting.
No. Because by changing H from emulator to halt decider, you have
changed
P.
When H(P,P) correctly determines that P would never reach its "ret"
instruction (AKA final state) this makes H a halt decider for this
input
by definition:
computation that halts … the Turing machine will halt whenever it
enters
a final state. (Linz:1990:234)
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
GUR is repeatedly proved:
olcott can never provide a real halting decider except a verbal one.
Thanks olcott.
This one proves that H(P,P) does correctly determine that H(P,P)==0 is
correct:
H(P,P)==0 as a pure function of its inputs is fully operational V2
On 6/17/2022 9:31 PM, olcott wrote:
Except it isn't since H(P,P) returns 0, saying that P(P) is non-halting,
when P(P) will halt when H(P,P) returns 0.
If H(P,P) isn't asking about P(P), then you don't have the right
function P, as the Linz definition of P is that it will ask about that.
(X) H(P,P) correctly determines (in a finite number of steps) that the
correct and complete x86 emulation of its input would never reach the
"ret" instruction (AKA final state) of this input.
(Y) computation that halts … the Turing machine will halt whenever it
enters a final state. (Linz:1990:234)
(Z) H(P,P) has correctly determined that its input is non-halting.
When we know that X & Y proves Z and we know X & Y then Z is proved.
Failing to agree with this last line is sufficient evidence of dishonesty.
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
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