Re: Unconventional partial halt decider and grounding to a truthmaker

On 5/17/2024 7:50 AM, Ben Bacarisse wrote:

 When I did engage with him it was to try to pin down what he was really
saying and, after years of back-and-forth, he made two unequivocal
statement that, to my mind, render all subsequent discussion pointless.
First, when asked
      "Here's the key question: do you still assert that H(P,P) == false is
     the 'correct' answer even though P(P) halts?"
 He replied:
     "Yes that is the correct answer even though P(P) halts."
 

Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that a function is
computable if there exists an algorithm that can do the job of the
function, i.e. *given an input of the function domain it can return the*
*corresponding output* https://en.wikipedia.org/wiki/Computable_function
typedef int (*ptr)();  // ptr is pointer to int function
00 int H(ptr x, ptr x)
01 int P(ptr x)
02 {
03   int Halt_Status = H(x, x);
04   if (Halt_Status)
05     HERE: goto HERE;
06   return Halt_Status;
07 }
08
09 int main()
10 {
11   P(P,P);
12 }
My reviewers have never been aware of the fact computable functions
are not allowed to report on the behavior of the computation they
themselves are contained within because deciders cannot take actual
Turing Machines as inputs.
This makes the behavior of the executed P(P) moot and instead H must
report on the behavior that the input to H(P,P) specifies.
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 or may not include one or more recursive simulations where H
correctly simulates itself simulating D in the order specified by the
x86 instructions of H.
This conclusively proves that D correctly simulated by H cannot possibly
reach its own line 06 and halt to everyone with sufficient knowledge
of the semantics of the C programming knowledge.
*Introduction to the Theory of Computation, by Michael Sipser*
https://www.amazon.com/Introduction-Theory-Computation-Michael-Sipser/dp/113318779X/
On 10/13/2022 11:29:23 AM
*MIT Professor Michael Sipser agreed these verbatim words are correct*
(He has neither reviewed nor agreed to anything else in this paper)
    If simulating halt decider H correctly simulates its input D until H
    correctly determines that its simulated D would never stop running
    unless aborted then
    H can abort its simulation of D and correctly report that D specifies
    a non-halting sequence of configurations.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer