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In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run
forever. https://en.wikipedia.org/wiki/Halting_problem
This message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations as noted. All Rights Reserved except as stated
in the message sig.
On 26/09/2025 19:15, olcott wrote:
In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program and an
input, whether the program will finish running, or continue to run
forever. https://en.wikipedia.org/wiki/Halting_problem
Not exactly. The nature of the machine is left unspecified as stated,
and a physical machine could be said to transition from some states to themselves rather than halting because they vary across time which
relations among objects of formal systems don't.
I think you need to include a restriction on the machines to those that
have an actually irrevocable "exhaustion" signal strictly correlated
with state-constancy. Perhaps its not enough even then when you want to
couch the problem in terms of physical machines, and perhaps it's not
useful because of the inseparability of the machine from its generalised environment "the universe" where we must talk of mere persistent
structures (which is subjective anyway).
Perhaps it's best to discuss computability only in terms of formal
systems containing objects some having ultimate definientia and some not thereby leaving physical computers for discussions of the enforcement of local structure on the universe ("security"). It's much easier and
agreeing anything about it isn't rendered impossible by the absence of a certainly-accurate physical theory. About formal systems we can, to some extent, discuss relations that are closely constrained to the discrete
by a very complex common brain structure and decades of common
linguistic conditioning. That's even though there are obviously similar limitations just as there are with discussion of mechanical computers
because a quorum of logicians is the computer and we will perceive them
as unreliable, distractable, and bounded then exclude all considerations
of disobedience and of persistence of physical structure in our discourse.
There are interesting further problems that become apparent with the
formal systems approach which I haven't seen discussions of before, and
which I'm too amateur to describe here for fear of embarrassing myself.
--
Tristan Wibberley
The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
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of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.
On 10/9/2025 10:52 AM, Tristan Wibberley wrote:
See my new post
[Halting problem proof converted to Liar Paradox
--- 2004 post converted to C]