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On 5/13/2025 1:20 PM, Mike Terry wrote:No, as that is not a program, DD calls the specific HHH that it has been built on,On 13/05/2025 19:00, Richard Heathfield wrote:The input being decided by HHH(DD) includes DDOn 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?
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DDD doesn't do anything interesting.
I wasn't referring to DDD specifically, but in general.
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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.
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<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.
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Real halting is a property of just the input being decided, as is
calling its own emulator in recursive simulation.
The input being decided by HHH1(DD) DOES NOT INCLUDEBut it still calls the exact sane HHH, and thus is the same program.
DD calling its own emulator in recursive simulation.
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.
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Mike.
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