Re: Every D(D) simulated by H presents non-halting behavior to H ###

On 5/27/24 11:43 AM, olcott wrote:

On 5/27/2024 9:58 AM, Richard Damon wrote:

On 5/27/24 10:39 AM, olcott wrote:

 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 either pure simulator H or pure function H. This
was done because many reviewers used the shell game ploy to endlessly
switch which H/D pair was being referred to.
 Correct Simulation Defined
    This is provided because many reviewers had a different notion of
    correct simulation that diverges from this notion.
     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.

And how do you apply that to a TEMPLATE that doesn't define what a call H means (as it could be any of the infinite set of Hs that you can instantiate the template on)?
Do you mean the specific instance that this particular H generates? In which case each H simulates a DIFFERENT input, and thus the simulations can not be used for any other input.

 When we see that D correctly simulated by pure simulator H would remain
stuck in infinite recursive simulation then we also know that less than
an infinite number of steps is not enough steps for D correctly
simulated by pure function H to reach its own simulated final state at
line 06 and halt.

And by the previous comment, either you simulation isn't defined, or the simulation by the pure simulator doesn't provide behavior for the simulation by the finite simulation done by other Hs.
It is IMPOSSIBLE for any of your Hs to actually simulate the TEMPLATE D beyond the call H instruction, as there is no defined code for H in the template, only in instances of it.
When we accept that your simulation MUST be of the instance given, and NOT the "template", then all you have proved is that all the finite simulators just didn't simulate far enough to reach a possible final state, as simulations of different imputs do not logically correlate to each other allowing inferences across them.

 

When D correctly simulated by pure simulator H cannot possibly reach
its own simulated final state at line 06 and halt in an infinite number
of simulated steps we can conclude that less than an infinite number of
steps is also not enough steps for D to halt.
>

>
But ONLY for THAT D, the one built on the pure simulator that never aborts.
>

 https://en.wikipedia.org/wiki/Shell_game
*I updated my words to address your persistent shell-game ploy*
 The above template refers to an infinite set of H/D pairs where D is
correctly simulated by either pure simulator H or pure function H. This
was done because many reviewers used the shell game ploy to endlessly
switch which H/D pair was being referred to.
 

And thus you need to either fix your definition of "simulation" to define what happens when you "simulate" an infinte set of different code, or fix your logic where you try to use logic about the simulation of DIFFERENT specific inputs to derive behaviors of an input that is objectively different then the simulation you are doing here.
In other words, your attempt to define your H and D as Infinite sets has is incompatible with your definition of "Correct Simulation" and you need to resolve this.
It seems your problem is that you are having a hard time to find the words to express what you mean, because what you are thinking about is just a logical contradiction, which gets revealed by trying to be precise in the words, so you need to keep the words fuzzy.
You can't simulate the instructions of a template that don't exist because they are variable based on the machine the template will be instantiated on. You need to either change your definition of what "Correct Simulation" means on the template, or define that you are processing specific instances, and accept that this means that each instance is a totally seperate problem, and you can't just argue across the problems.