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When it is understood that D correctly simulated by H is the behavior
that H must report on then the halting problem`s otherwise impossible
input is correctly determined to be non-halting.
We can know that D correctly simulated by H must have different behavior
than D(D) directly executed in main() because we can see (in its
execution trace shown below) exactly how the pathological relationship
between D and H changes the behavior of D relative to H.
*Can D correctly simulated by H terminate normally*
The x86utm operating system based on an open source x86 emulator. This
system enables one C function to execute another C function in debug
step mode.
// The following is written in C
//
01 typedef int (*ptr)(); // pointer to int function
02 int H(ptr x, ptr y) // uses x86 emulator to simulate its input
03
04 int D(ptr x)
05 {
06 int Halt_Status = H(x, x);
07 if (Halt_Status)
08 HERE: goto HERE;
09 return Halt_Status;
10 }
11
12 void main()
13 {
14 H(D,D);
15 }
*Execution Trace*
Line 14: main() invokes H(D,D);
*keeps repeating* (unless aborted)
Line 06: simulated D(D) invokes simulated H(D,D) that simulates D(D)
*Simulation invariant*
D correctly simulated by H cannot possibly reach past its own line 06.
*Termination Analyzer H is Not Fooled by Pathological Input D*
https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not
_Fooled_by_Pathological_Input_D
--
Copyright 2023 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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