Re: And those are the facts

On 6/13/25 11:02 AM, Mr Flibble wrote:

A simulating halt decider (SHD) must always halt (i.e. provide a halting
decision about its input) irregardless of whether or not its input halts.
 And those are the facts.
 /Flibble

And to BE a CORRECT decider, its answer must match the criteria defined for the input, which for a Halt Decider, is does the program represented by the input halt.
Thus, an input that a SHD that returns the code for non-halting, must never halt when actually run.
Since for the H/D pair that has been the focus here for years, if H(D) returns 0, D will halt, H(D) returning 0 can not be a correct answer.
PERIOD. THAT IS THE FACTS.
The point is that a SHD can not correctly simulate a non-halting input, and return 0 as required, and thus if the defining condition of the SHD is that it is based on its own correct simulation, it can NEVER return 0, as that is just proven to be a contradiction to its requirements.
Since non-halting inputs exist, that says that a SHD based on just its own correct simulation of its input is just a self-contradiction, and thus the criteria is incorrect.