On 1/9/24 12:33 PM, olcott wrote:
On 1/9/2024 8:42 AM, Mikko wrote:
On 2024-01-09 03:16:49 +0000, olcott said:
04 int D(ptr x)
05 {
06 int Halt_Status = H(x, x);
07 if (Halt_Status)
08 HERE: goto HERE;
09 return Halt_Status;
10 }
11
12 void main()
13 {
14 H(D,D);
15 }
What is step by step line-by-line correct sequence of steps
when the simulation of D by H reaches line 06?
There are two possibilities.
For a superficial simulation it is sufficient to
determine what H(x, x) returns and assign that
to Halt_Status and then simulate forward.
For detailed simulation the calling sequence to H must be
simulated and then one by whatever instructions there are
in H.
Mikko
OK great so you are saying that when D correctly simulated by H
reaches line 06 that H must simulate the invocation of H(D,D).
That <is> correct. It also means that D correctly simulated
by any H that can possibly exist cannot possibly reaches its
own line 09, thus cannot possibly reach its own final instruction
and terminate normally, thus never halts.
You are making the unwarrented assumption that an H CAN simulate the
input correctly and also be a decider.
Any H that simulates the input (based on itself) doesn't answer, and any
H that answers, didn't simulate its input corrctly, as shown by
continuing this exact simulation with another pure simulator.
Note, the definition of D is that it is based on a particular H, not
whatever simulator is looking at it. THAT definition is actually
impossible to build as an independent machine.
Your changing D to match the H is what creates the "self-reference" that
makes the question not have an answer and thus incorrect to ask. This
shows that an H meeting your requirement just doesn't exist, like the
Barber that shaves everone who doesn't have themselves.
It isn't the question of who a barber shaves that is invalid, it is
trying to choose THAT Barber, who just can't exist.
THe Halting Question is perfectly valid for any input that actually
exists, we just can't make a D from an H that doesn't exist.
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