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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Why do people here insist on denying these verified facts?
Date: Sat, 22 Jun 2024 09:31:45 -0500
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https://www.amazon.com/Introduction-Theory-Computation-Michael-Sipser/dp/113318779X/

To understand this analysis requires a sufficient knowledge of
the C programming language and what an x86 emulator does. HHH0
and HHH1 have this criteria as their algorithm:

<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
   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.
</MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>

On 10/14/2022 7:44 PM, Ben Bacarisse wrote:
 > I don't think that is the shell game. PO really /has/ an H
 > (it's trivial to do for this one case) that correctly determines
 > that P(P) *would* never stop running *unless* aborted.
 >

Ben only agrees that the criteria is met for the input. He
does not agree that the criteria has been meet for non-inputs.

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

*That seems to say that non-inputs do not count*

*Here is the verified facts that everyone denies*
*Here is the verified facts that everyone denies*
*Here is the verified facts that everyone denies*
*Here is the verified facts that everyone denies*

void DDD()
{
   HHH0(DDD);
}

int main()
{
   Output("Input_Halts = ", HHH0(DDD));
   Output("Input_Halts = ", HHH1(DDD));
}

It is a verified fact that the behavior that finite string DDD
presents to HH0 is that when DDD correctly emulated by HH0
calls HH0(DDD) that *THIS CALL DOES NOT RETURN*

It is a verified fact that the behavior that finite string DDD
presents to HH1 is that when DDD correctly emulated by HH1
calls HH0(DDD) that *THIS CALL DOES RETURN*


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