Re: Pathological self-reference changes the semantics of the same finite string.

Op 30.Aug.2024 OM 14:57 screech Wolcott:

On 8/30/2024 3:11 AM, Mikko wrote:

On 2024-08-29 17:53:44 +0000, olcott said:
>

I just proved that the basic notion of finite strings
having unique meanings independently of their context
is incorrect.

>
The context is the halting problem.

 The behavior of
the directly executed DDD and executed HHH
is different from the behavior of
the emulated DDD and the emulated HHH
 and all four of them are emulated by the world
class x86 emulator libx86emu

And the unmodified world class emulator showed that the input (DID based on HEH) has a halting behaviour.

 It is easy to see that when the executed HHH emulates
DDD that it does this correctly when we look at the
execution trace and see the the first four instructions
of DDD are listed.
 _DDD()
[00002172] 55         push ebp      ; housekeeping
[00002173] 8bec       mov ebp,esp   ; housekeeping
[00002175] 6872210000 push 00002172 ; push DDD
[0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
[0000217f] 83c404     add esp,+04
[00002182] 5d         pop ebp
[00002183] c3         ret
Size in bytes:(0018) [00002183]
 New slave_stack at:1038c4
Begin Local Halt Decider Simulation   Execution Trace Stored at:1138cc
[00002172][001138bc][001138c0] 55         push ebp      ; housekeeping
[00002173][001138bc][001138c0] 8bec       mov ebp,esp   ; housekeeping
[00002175][001138b8][00002172] 6872210000 push 00002172 ; push DDD
[0000217a][001138b4][0000217f] e853f4ffff call 000015d2 ; call HHH(DDD)
New slave_stack at:14e2ec
[00002172][0015e2e4][0015e2e8] 55         push ebp      ; housekeeping
[00002173][0015e2e4][0015e2e8] 8bec       mov ebp,esp   ; housekeeping
[00002175][0015e2e0][00002172] 6872210000 push 00002172 ; push DDD
[0000217a][0015e2dc][0000217f] e853f4ffff call 000015d2 ; call HHH(DDD)
Local Halt Decider: Infinite Recursion Detected Simulation Stopped
 Then this emulated DDD calls an emulated HHH(DDD).
It is easy to see that when the executed HHH emulates
itself emulated DDD that it does this correctly when we
look at the execution trace and see the the first four
instructions of DDD are listed again.

And after a few recursions HEH sees a 'special condition' which makes that its stops the simulation.
This is a modification of the world class simulator, which makes the simulation incorrect, because now it stops before the simulated input could halt.
Since the unmodified world class simulator showed a halting behaviour, the modified simulator must be incorrect.
It stops the simulation one cycle too soon.