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On 13/05/2025 19:00, Richard Heathfield wrote:On 13/05/2025 18:12, dbush wrote:On 5/13/2025 1:06 PM, Richard Heathfield wrote:On 13/05/2025 17:21, dbush wrote:On 5/13/2025 12:01 PM, olcott wrote:
<snip>
The actual reasoning why HHH is supposed to report
on the behavior of the direct execution of DD()
instead of the actual behavior that the finite
string of DD specifies:
Quite simply, it's the behavior of the direct execution that we want to know about.
Why?
DDD doesn't do anything interesting.
I wasn't referring to DDD specifically, but in general.
He's claiming *in general* that H(X) is supposed to report on "X simulated by H" instead of the
direct execution of X,
...where the former is obviously less interesting than the latter. Fair enough.
<snip>
Right! PO's defintion of PO-halting (based on what "the simulator" does) makes halting a property
of both the input being decided /and/ the machine doing the deciding.
Real halting is a property of just the input being decided, as is required to be the case with any
"decision problem" such as HP. His definition is a total non-starter. That's before we even point
out that an input for HP doesn't even have "its simulator" in general.
Mike.
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