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*Mike understood this perfectly*And you dishonestly left out the part that immediately follows where he states that you are wrong:
On 5/14/2025 7:36 PM, Mike Terry wrote:
--------- Sipser quote -----
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.
----------------------------
we can easily interpret that as saying exactly what I said a SHD
does above. It tells PO that in the tight loop example, H correctly
simulates as far as [A], at which point it correctly determines that
"its simulated input would never stop running unless aborted", so
it can decide "non-halting".
All correct and natural, and no deliberately
false premises to mislead PO.
On 5/14/2025 7:36 PM, Mike Terry wrote:
https://al.howardknight.net/? STYPE=msgid&MSGI=%3C1003cu5%242p3g1%241%40dont-email.me%3E
PO's problem is his misinterpretation of "its simulated input would never stop running unless aborted". In the case of his HHH/DD, the simulated input (DD) /does/ stop running if simulated far enough, but HHH simply /doesn't/ go far enough because PO has mistakenly decided he's seen some pattern that implies non-halting in the trace. [A pattern akin to the "tight loop" pattern, except that the tight loop pattern is sound, while his pattern is unsound, matching on a halting input. Simples!]This proves, as you yourself said:
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