--- Vladimir Nesov <[EMAIL PROTECTED]> wrote:
> On Sat, May 10, 2008 at 2:09 AM, Matt Mahoney <[EMAIL PROTECTED]>
> wrote:
> >
> > --- Vladimir Nesov <[EMAIL PROTECTED]> wrote:
> >>
> >> (I assume you mean something like P((P,y))=P(y)).
> >>
> >> If P(s)=0 (one answer to all questions), then P((P,y))=0 and P(y)=0
> >> for all y.
> >
> > You're right. But we wouldn't say that the trivial language P =
> {0,1}*
> > "understands" anything. That is a problem with my formal definition
> > of "understanding".
> >
>
> Then make a definition that fits your claim. As currently stated, it
> looks erroneous to me, and I can't see how it's possible to fix that
> without explicating your assertion mathematically.
OK, let me make more clear the distinction between running a program and
simulating it. Say that a program P simulates a program Q if for all y,
P((Q,y)) = "the output is "+Q(y) where + means string concatenation. In
other words, given Q and y, P prints not Q(y) but a statement describing
what the output Q(y) would be. Then I claim there is no finite state
machine P that can simulate itself (including the trivial case). P needs
as many states as Q to simulate it, plus additional states to print "the
output is ".
I also claim that "P understands Q" can be reasonably interpreted as "P
can simulate Q", but I can't prove it :-)
-- Matt Mahoney, [EMAIL PROTECTED]
-------------------------------------------
agi
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