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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Every D(D) simulated by H presents non-halting behavior to H
Date: Sun, 5 May 2024 12:02:25 -0500
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The x86utm operating system: https://github.com/plolcott/x86utm enables
one C function to execute another C function in debug step mode.
Simulating Termination analyzer H simulates the x86 machine code of its
input (using libx86emu) in debug step mode until it correctly matches a
correct non-halting behavior pattern proving that its input will never
stop running unless aborted.

Can D correctly simulated by H terminate normally?
00 int H(ptr x, ptr x)  // ptr is pointer to int function
01 int D(ptr x)
02 {
03   int Halt_Status = H(x, x);
04   if (Halt_Status)
05     HERE: goto HERE;
06   return Halt_Status;
07 }
08
09 int main()
10 {
11   H(D,D);
12 }

*Execution Trace*
Line 11: main() invokes H(D,D);

*keeps repeating* (unless aborted)
Line 03: 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 03.

The above execution trace proves that (for every H/D pair of the
infinite set of H/D pairs) each D(D) simulated by the H that this D(D)
calls cannot possibly reach past its own line 03.

*Shown by ordinary software engineering* When the directly executed
H(D,D) aborts simulating its input then all of the nested simulations
(if any) immediately totally stop running and no simulated H ever
returns any value to any simulated D.

 From this we can definitely know that every D(D) of the infinite set
of H/D pairs where this D(D) is simulated by the H that this D(D) calls
that this D(D) presents non-halting behavior to this H.

*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 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer