Re: D correctly simulated by H never halts

On 5/28/2024 4:11 AM, Fred. Zwarts wrote:

Op 27.mei.2024 om 16:00 schreef olcott:

On 5/27/2024 3:57 AM, Fred. Zwarts wrote:

Op 26.mei.2024 om 17:42 schreef olcott:

On 5/26/2024 9:43 AM, Fred. Zwarts wrote:

Op 26.mei.2024 om 15:20 schreef olcott:

On 5/26/2024 6:01 AM, Fred. Zwarts wrote:

Op 26.mei.2024 om 06:19 schreef olcott:

On 5/25/2024 2:32 AM, Fred. Zwarts wrote:

Op 23.mei.2024 om 18:52 schreef olcott:

typedef int (*ptr)();  // ptr is pointer to int function in C
00       int H(ptr p, ptr i);
01       int D(ptr p)
02       {
03         int Halt_Status = H(p, p);
04         if (Halt_Status)
05           HERE: goto HERE;
06         return Halt_Status;
07       }
08
09       int main()
10       {
11         H(D,D);
12         return 0;
13       }
>
The above template refers to an infinite set of H/D pairs where D is
correctly simulated by pure function H. This was done because many
reviewers used the shell game ploy to endlessly switch which H/D was
being referred to.
>
*Correct Simulation Defined*
This is provided because every reviewer had a different notion of
correct simulation that diverges from this notion.
>
In the above case a simulator is an x86 emulator that correctly emulates
at least one of the x86 instructions of D in the order specified by the
x86 instructions of D.
>
This may include correctly emulating the x86 instructions of H in the
order specified by the x86 instructions of H thus calling H(D,D) in
recursive simulation.
>
*Execution Trace*
Line 11: main() invokes H(D,D); H(D,D) simulates lines 01, 02, and 03 of
D. This invokes H(D,D) again to repeat the process in endless recursive
simulation.
>

>
Olcott's own words are that the simulation of D never reaches past line 03. So the lines following line 03 do not play a role and, therefore, can be removed without changing the claim. This leads to:
>
typedef int (*ptr)();  // ptr is pointer to int function in C
00       int H(ptr p, ptr i);
01       int D(ptr p)
02       {
03         return H(p, p);
04       }
05
06       int main()
07       {
08         H(D,D);
09         return 0;
10       }
>
>
What we see is that the only property of D that is used is that it is a parameter duplicator. (Is that why it is called D?). H needs 2 parameters, but it can be given only one input parameter, so the parameter duplicator is required to allow H to decide about itself.
>
>
>
Of the infinite set of H that simulate at least one step, none of them, when simulated by H, halts, because none of them reaches its final state. Olcott's claim is equivalent to the claim of non-halting behaviour of H.
This means that a simulating halt-decider is a bad idea, because the decider itself does not halt.

>
Not at all.
    A simulator is an x86 emulator that correctly emulates 1 to N of the
    x86 instructions of D in the order specified by the x86 instructions
    of D. This may include M recursive emulations of H emulating itself
    emulating D.
>
    This means that D cannot possibly reach its own line 06 and halt
    in any finite steps of correct simulation. H is free to halt at
    any time after these N finite steps of correct simulation.
>
>

>
D does not reach it own line 04 because the simulation of H does not return to D. So, it shows that the simulation of H does not reach it final state, which proves that H does not halt.

>
Your transformation would have been acceptable if you retained the
fact that H is a pure function that always halts and returns some value.
>

>
Since H is required to halt, but H shows that H does not halt (because the simulation of H never reaches its final state), the conclusion must be that there is no such H.

>
 >
>
When D correctly simulated by pure simulator H remains stuck in infinite
recursive simulation then we also know that D never reaches its own line
06 and halts in less than an infinite number of correctly simulated
steps.
>
This is what I had in mind all along. Because I am a relatively terrible
communicator it takes me a very long time to translate my intuitions
into simple words.
>
>

typedef int (*ptr)();  // ptr is pointer to int function in C
00       int H(ptr p, ptr i);
01       int D(ptr p)
02       {
03         return H(p, p);
04       }
05
06       int main()
07       {
08         H(D,D);
09         return 0;
10       }
>
We see that the requirements for H are contradictory.

>
*Not at all, I just did not explain us clearly enough*
>
When we hypothesize that H is a pure simulator we see that D correctly

 ... we see that H correctly ...
 

simulated by pure simulator H remains stuck in recursive simulation thus
never reaches its own simulated final state at its line 06 and halts. In

 (the line 06 is different in my example)
 

this case H does not halt, thus is neither a pure function nor a
decider.
>
 From this we correctly conclude that D correctly simulated by pure

 ... we correctly conclude that H correctly simulated by ...
 

function H never reaches its simulated final state at its own line 06

 (The line 06 is different in my example)
 

and halts in Less than an infinite (AKA finite) number of simulated
steps. Here is a concrete example of that:
>
https://en.wikipedia.org/wiki/Googolplex
When pure function H correctly simulates a Googolplex ^ Googolplex
number of steps of D, then D never reaches its simulated final state

 ... of H, then H never reaches its simulated final state
 

at its own line 06 and halts. Pure function H halts after this finite

 (The line 06 is different in my example)
 

number of steps of correct simulation.

 The simulation of H never reaches its final state. Whether the direct execution of H halts is the wrong question.
 

typedef int (*ptr)();  // ptr is pointer to int function in C
00       int H(ptr p, ptr i);
01       int D(ptr p)
02       {
03         int Halt_Status = H(p, p);
04         if (Halt_Status)
05           HERE: goto HERE;
06         return Halt_Status;
07       }
08
09       int main()
10       {
11         H(D,D);
12         return 0;
13       }
No it is not the wrong question.
D correctly simulated by pure simulator H never reaches it own simulated final state at line 06 and halts and H does not halt.
D correctly simulated by pure function H never reaches it own simulated final state at line 06 and halts and H does halt.
The reason it is not the wrong question that all deciders must halt.

>
In other words when the *INPUT* to H(D,D) is correctly simulated by
either pure simulator H or pure function H this correctly simulated
*INPUT* never halts no matter what, thus the INPUT to H(D,D) is
definitely non halting.

 D is non halting, because the simulation of H does not reach its final state and therefore does not return to D. So, the hypothesis that H is a pure simulator that halts turns out to be

A claim that I never made.

contradictory because the simulation of H shows that H does not reach its final state, so, no such H exists.
 

H is a pure simulator or a pure function.
D correctly simulated by pure function H never reaches it own simulated
final state at line 06 and halts and H does halt.
The reason for needing the pure simulator H is to see that D correctly
simulated by H never reaches its own final state and halts UNDER ANY
CIRCUMSTANCES.
When D have For 1 to ∞ steps correctly simulated by some H then D never
reaches its own final state at line 06 and halts.
When H is a pure simulator then H does not halt.
When H is a pure function then H halts.
In none of these cases does D simulated by H halt.

>
*This is STEP ONE of my four step proof*
>

 

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