Re: The philosophy of computation reformulates existing ideas on a new basis ---

On 11/4/24 9:31 AM, olcott wrote:

On 11/4/2024 8:14 AM, Mikko wrote:

On 2024-11-03 14:39:35 +0000, olcott said:
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On 11/3/2024 6:11 AM, Mikko wrote:

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It is not clear at all unless you specify how those finite
strings specify the actual behaviour.

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That is why I used to fully defined semantics of the x86
language to make this 100% perfectly unequivocal.

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It does not add any clarity to the last paragraph before
my previous comment.
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 I always respond to the immediately preceding paragraph.
The finite strings specify actual behavior on the basis
of the semantics of the x86 language.

But to do so, you need ALL the code, and the emulation done (or at least looked at) must be non-aborting, or it isn't by the semantics.

 

A few lines of x86 code express complex algorithms
succinctly enough that human minds are not totally
overwhelmed by far too much tedious detail.
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It is not pspecified
in the usual formulation of the problem. Also note that
the behaviour exists before those strings so "describe"
should be and usually is used instead of "specify". The
use of latter may give the false impression that the behaviour
is determined by those strings.
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In order for any machine to compute the mapping from
a finite string it must to so entirely on the basis
of the actual finite string and its specified semantics.
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The finite string input to HHH specifies that HHH
MUST EMULATE ITSELF emulating DDD.
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The finite string input to HHH1 specifies that HHH1
MUST NOT EMULATE ITSELF emulating DDD.
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Unless HHH rejects its input DDD as non halting the
executed DDD never stops running. This itself proves
that HHH is correct and that DDD is not the same
instance as the one that HHH rejected.
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It is true that when we construe the halting criteria as
requiring taking into account how a pathological relationship
changes the behavior of the input instead of simply ignoring
this behavior change that pathological inputs become decidable
as non-halting.

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It is true that doing that means leaving the halting proble unsolved.
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The HP proofs are refuted by my work.

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No. Talking about something else does not refute.
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 As long as it is understood that it has always simply been
incorrect to construe that behavior of the input finite
string as anything other than the actual behavior that this
finite string specifies which includes HHH emulating itself
emulating DDD then I have refuted the original proofs.
 (a) Finite string of x86 machine code DDD +
(b) The semantics of the x86 language +
(c) DDD is calling its own termination analyzer
∴ HHH is correct to reject its input as non-halting
 We can only get to the behavior of the directly
executed DDD() by ignoring (b) or (c)
 

This is not quite the same ting as solving the halting problem.

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It is very far even from any thinking about the possibility to solve
the halting problem.
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