It is meaningful, because j supports arrays of unbounded length, and it
does not support arrays of infinite length (though that has been
proposed). For example, it is possible to implement a turing machine in
j, by representing only the finitely many cells which have been visited so
far. As the number of steps simulated increases without bound, so too may
the memory requirements; but so long as the former is finite, the latter
must be, too. And there is no expectation that you will be able to
simulate infinite steps of a turing machine in finite real time.
(In this respect, extant implementations of j are not and can not be
turing-complete, but that is irrelevant.)
-E
On Tue, 8 Feb 2022, Raul Miller wrote:
If we are talking about equivalence to a turing machine --
https://en.wikipedia.org/wiki/Turing_machine -- I do not think this is
a meaningful distinction.
Thanks,
--
Raul
On Tue, Feb 8, 2022 at 3:51 PM Elijah Stone <elro...@elronnd.net> wrote:
That is not quite right. We do not need to explicitly represent infinite
arrays; we only need array length to be unbounded, such that the length of
a given array can grow without bound (but finitely) over a finite amount
of time. See limit definition.
-E
On Tue, 8 Feb 2022, Raul Miller wrote:
> On Tue, Feb 8, 2022 at 4:30 AM Elijah Stone <elro...@elronnd.net> wrote:
>> Can anyone come up with something which does not require infinite arrays?
>
> Technically, any system which does not support infinite time and
> infinite space is not turing complete.
>
> That said, in most contexts, we take "infinite" to mean "larger than I
> need for the example(s) I am concerned about".
>
> FYI,
>
> --
> Raul
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
