note
tilly
I find your distinction between solvability and
decidability somewhat interesting. I have not heard
the distinction drawn that way. It has been a few years
since I last looked at a book on this subject (and I gave
away most of my math books about 4 years ago, so I don't
even have one to look this up in right now), but I
would think I would have remembered something like that.<p>
So I did a quick Google search. And the funny thing is
that I found lots of presentations online that disagreed
with your proposed usage. I found none that agreed. For a
random instance
[http://students.cs.byu.edu/~cs252ta/Lecture14.pdf|this
lecture] states directly that the Halting problem is not
solvable.<p>
And even when I look at your links, they say nothing about
finite versus infinite. The classification they draw goes
like this. A decision problem is a problem whose answers
are all yes/no. A decidable problem a decision problem that
is solvable. Solvable problems differ from decision
problems in that solvable problems are not just limited to
yes/no answers.<p>
The fact that infinite answers are not accepted either for
definitions of decidability or solvability is underscored
by
[http://www.cis.ohio-state.edu/~gurari/theory-bk/theory-bk-onese4.html|this
lecture]. They are very explicit about the fact that
solvability and decidability both require that all of the
computations involved halt. In other words you need to
get an answer in due time.<p>
Now you wouldn't just be making up your finite/infinite
distinction, would you? Do you have a verifiable source
you are willing to quote showing that someone else out
there agrees with the usage you are claiming?
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