Re: Proving the: Simulating termination analyzer Principle

On 4/5/25 4:51 PM, olcott wrote:

*Simulating termination analyzer Principle*
It is always correct for any simulating termination
analyzer to stop simulating and reject any input that
would otherwise prevent its own termination.
 void DDD()
{
    HHH(DDD);
    return;
}
 Anyone knowing the C programming language knows
that DDD simulated by HHH by any correct pure
simulator would prevent HHH from terminating.
 

Which means it must be CORRECT, per the definition of the mapping that the decider is supposed to be deciding on, which for a Halt Decider/Termination Analyzer is the mapping of the direct execution of the program described by the input. It MUST accept ANY program that will halt by the definition, and must any program that will never halt, even after running for an unbounded number of steps.
The partial emulation of the input doesn't matter, and the input MUST represent a COMPLETE program, and thus for your above, MUST include the code for the SPECIFIC HHH that it is designed to be foiling, which is your orignal HHH defined in Halt7.c which DOES abort its emulation and returns 0.
Since that direct execution will clearly halt (as shown by the actually correct emulation done by HHH1) we can say that you HHH, which DOES abort its emulation, did not have the proper justifcatio for its behavior.
Note, since DDD calls that specific HHH, the fact that HHH behaves that was is what keeps it from preventing its own termination.
Your logic makes the strawman fallacy of presuming you change the input when you change HHH, but that violates the definition of DDD being a program.
Note, your final paragraph is just a collection of word salad, as your HHH is NOT a "pure simulator" but only a partial simulator, so is self-contradictory.
It seems you want to look at a totally different version of the input, where both HHH are actually correct simulators, and yes, in that case DDD will be non-haltig, but that HHH fails to be the needed decider, and this DDD is not the same DDD as given to your actual HHH, as your actual HHH gives an answer, and thus doesn't do that actually correct simulation.
So, all you are doing is proving your ignorance of what you are talking about because you don't understand the meaning of the words, and that you have chosen to just lie about what you are doing as you know you are changing definitions, and thus using the strawman argument that you know to be invalid, as you keep on projecting and accusing everyone else of committing while you are doing it yourself.