Re: HHH(DDD) sees the exact same behavior pattern as HHH(Infinite_Recursion)

Op 28.jul.2024 om 16:32 schreef olcott:

It is ridiculously stupid to expect the correct emulation
of a non-halting input to end.

It is also ridiculous to expect that a halting program must be aborted to prevent non-termination.

 HHH(DDD) is the exact same pattern with Infinite_Recursion()
where there are no conditional branch instructions that would
prevent the first three instructions of Infinite_Recursion()
from endlessly repeating.
 void Infinite_Recursion()
{
   Infinite_Recursion();
}
 

HHH has the same pattern as
void Finite_Recursion (int N) {
   if (N > 0) Finite_Recursion (N - 1);
}
Both HHH and Finite_Recursion halt after a few recursions.
That is because of the conditional branch instructions within HHH, when HHH simulates itself, as part of the input.

_Infinite_Recursion()
[0000215a] 55         push ebp      ; 1st line
[0000215b] 8bec       mov ebp,esp   ; 2nd line
[0000215d] e8f8ffffff call 0000215a ; 3rd line
[00002162] 5d         pop ebp
[00002163] c3         ret
Size in bytes:(0010) [00002163]
 Begin Local Halt Decider Simulation   Execution Trace Stored at:113934
[0000215a][00113924][00113928] 55         push ebp      ; 1st line
[0000215b][00113924][00113928] 8bec       mov ebp,esp   ; 2nd line
[0000215d][00113920][00002162] e8f8ffffff call 0000215a ; 3rd line
[0000215a][0011391c][00113924] 55         push ebp      ; 1st line
[0000215b][0011391c][00113924] 8bec       mov ebp,esp   ; 2nd line
[0000215d][00113918][00002162] e8f8ffffff call 0000215a ; 3rd line
Local Halt Decider: Infinite Recursion Detected Simulation Stopped
 If you cannot see that the above x86 machine code proves that
it will never halt then you can't possibly understand what I
have been saying.
 The first three lines of _Infinite_Recursion() repeat and there
are no conditional branch in that sequence that can possibly keep
it from repeating forever.
 HHH(DDD) is the exact same pattern is shown below. The first
four lines of DDD repeat and there are are no conditional branch
in that sequence that can possibly keep it from repeating forever.

HHH has a very different pattern, because of the conditional branch instructions in the input, namely, those in HHH itself.
HHH halts, as is shown by the direct execution and by a correct simulation.

 =====
 void DDD()
{
   HHH(DDD);
}

DDD is a misleading and unneeded complication. It is easy to eliminate DDD:
        int main() {
          return HHH(main);
        }
This has the same problem. This proves that the problem is not in DDD, but in HHH, which halts when it aborts the simulation, but it decides that the simulation of itself does not halt.
It shows that HHH cannot possibly simulate itself correctly.

 _DDD()
[00002177] 55               push ebp      ; 1st line
[00002178] 8bec             mov ebp,esp   ; 2nd line
[0000217a] 6877210000       push 00002177 ; push DDD
[0000217f] e853f4ffff       call 000015d7 ; call HHH
[00002184] 83c404           add esp,+04
[00002187] 5d               pop ebp
[00002188] c3               ret
Size in bytes:(0018) [00002188]
 // executed HHH emulates 1st instance of DDD
New slave_stack at:10388d
Begin Local Halt Decider Simulation   Execution Trace Stored at:113895
[00002177][00113885][00113889] 55         push ebp      ; 1st line
[00002178][00113885][00113889] 8bec       mov ebp,esp   ; 2nd line
[0000217a][00113881][00002177] 6877210000 push 00002177 ; push DDD
[0000217f][0011387d][00002184] e853f4ffff call 000015d7 ; call HHH
 // emulated HHH emulates 2nd instance of DDD
New slave_stack at:14e2b5
[00002177][0015e2ad][0015e2b1] 55         push ebp      ; 1st line
[00002178][0015e2ad][0015e2b1] 8bec       mov ebp,esp   ; 2nd line
[0000217a][0015e2a9][00002177] 6877210000 push 00002177 ; push DDD
[0000217f][0015e2a5][00002184] e853f4ffff call 000015d7 ; call HHH
Local Halt Decider: Infinite Recursion Detected Simulation Stopped
 

HHH is programmed to print an incorrect message after two recursion. Apparently the programmer thought that two recursions is enough to prove an infinite recursion. But two differs from infinite.
One cycle later the simulated HHH would abort and halt, after which DDD would halt, too.
But olcott is dreaming of a non-aborting non-halting version of HHH and thinks that dreams are a correct substitute for logic.
No matter how much olcott wants it to be correct, or how many times olcott repeats that it is correct, it does not change the fact that such a simulation is incorrect, because it is unable to reach the end.
Olcott's own claim that the simulated HHH does not reach its end confirms it. The trace he has shown also proves that HHH cannot reach the end of its own simulation. So, his own claims prove that it is true that HHH cannot possibly simulate itself up to the end, which makes the simulation incomplete and, therefore, incorrect.
Sipser would agree that this incorrect simulation cannot be used to detect a non-halting behaviour.