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devel / comp.theory / What is a halt decider according to Olcott?

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o What is a halt decider according to Olcott?immibis

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What is a halt decider according to Olcott?

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From: news@immibis.com (immibis)
Newsgroups: comp.theory
Subject: What is a halt decider according to Olcott?
Date: Sat, 24 Feb 2024 10:04:13 +0100
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 by: immibis - Sat, 24 Feb 2024 09:04 UTC

In the standard view, a halt decider is:
* A Turing machine
* With two final states called Yes and No (or qy and qn, or choose your
own names)
* An alphabet that is complex enough to represent Turing machines and
their initial tapes
* When-so-ever the initial tape of the halt decider is a representation
of a Turing machine and input pair that halts, the halt decider halts in
the Yes state.
* When-so-ever the initial tape of the halt decider is a representation
of a Turing machine and input pair that does not halt, the halt decider
halts in the No state.
* When-so-ever the initial tape of the halt decider is not a
representation of a Turing machine and input pair, we do not care what
the halt decider does.

Obviously Olcott believes something about this definition needs to be
changed. What specific changes are needed?

Could Olcott please copy this definition, make the necessary changes to
make the problem solvable, and send it back?

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