Re: How do computations actually work?

On 25/05/2025 10:14, Mikko wrote:

On 2025-05-24 15:18:57 +0000, olcott said:

<snip>

All termination analyzers are required to report on the
behavior that their input finite string specifies.

 To report correctly. Though the input string to a termination analyzer usially is incomlete: the input string usually
specifies different behavours depending on the input that is
not shown to the termination analyzer, and the analyzer's
report must cover all of them.

I think 'input string' is ambiguous here.
It would be clearer if people used 'program string' if they mean the program whose halting behaviour is being investigated and reserved 'input string' for when they mean the data - that is:
The analyser must determine whether the program string would terminate if applied to the input string.
Clearer still would be to drop 'string' and set up a couple of unambiguous aliases:
The analyser must determine whether program P would terminate if applied to input tape T.
In the above, requoted here:
 > To report correctly. Though the input string to a termination
 > analyzer usially is incomlete: the input string usually
 > specifies different behavours depending on the input that is
 > not shown to the termination analyzer, and the analyzer's
 > report must cover all of them.
I can't decide which 'input string' means P and which means T.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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