Re: Rebutting the Sipser Halting Problem Proof

Op 15.sep.2024 om 16:23 schreef olcott:

 Rebutting the Sipser Halting Problem Proof
D(D) correctly reports its own halt status
 https://www.researchgate.net/ publication/364302709_Rebutting_the_Sipser_Halting_Problem_Proof
 

We can see that the first seven instructions of D emulated by H precisely match the first seven instructions of the x86 source-code of D. This conclusively proves that these instructions were emulated correctly.

Yes H makes a good start, but fails to complete the simulation, because of a bug in the code to recognise an infinite 'recursion'.

H detects that D is calling H twice in sequence with the same aguments. H also sees that thereare no conditional branch instructions from the beginning of D to its call to H that can possibly escape the repetition of this recursive simulation.

H fails to see that in-between the two beginnings of D, there are many conditional branch instructions, namely in the H called by D.
The simulation fails to properly simulate the call to H. This bug makes that H decides incorrectly that there is an infinite recursion.

Anyone sufficiently technically competent in the x86 programming language will agree that the above execution trace of D emulated by H shows that D will never stop running unless H aborts its emulation of D.

Yes, and anyone sufficiently technically competent in the x86 language will also see that this proves that H fails to correctly complete the simulation.
The bug in the code decides after two cycles that there are an infinite number of cycles, because it misses the conditional branch instructions in these cycles, because of the incorrect simulation that deviates from the semantics of the x86 language, with an improper simulation of the H called by D.
So, it misses the fact that the simulated H would also (incorrectly) see this 'special condition', after which it would also abort, after which it would return to D and D would halt.
The string w describes only one program and the semantics of the x86 language allows only one behaviour for this program.
This behaviour is 'halting', as proven by direct execution, by the simulation by the world class simulator and other simulations.
But H fails to reproduce this behaviour in its attempt to simulate itself. This proves that H deviates from the semantics of the x86 language in its simulation.
H cannot possibly simulate itself correctly up to the end.