On Wed, Dec 05, 2007 at 11:08:34PM +0100, Mirek Dobsicek wrote:
> > Each expression like that denotes now either a computable function from 
> > N to N, or as we have to expect something else. And we have to expect 
> > they are no computable means to distinguish which U_i represents 
> > functions from N to N, and which represents the other beast. 
> Can I say that the other beasts are only and only infinite loops? I
> assume that the machine cannot destroy itself, so it either stops after
> computing a computable function or enters some silly loop.

Not unless the total number of states was finite. In a Turing machine
case, the tape being infinite and readable/writeable allows the
machine to compute forever without entering a loop. For instance, a
program outputting the digits of Pi onto the tape computes forever and
never enters a loop (since Pi is irrational, periodic sequences of
digits are ruled out).


A/Prof Russell Standish                  Phone 0425 253119 (mobile)
UNSW SYDNEY 2052                         [EMAIL PROTECTED]
Australia                                http://www.hpcoders.com.au

You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To post to this group, send email to [EMAIL PROTECTED]
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at 

Reply via email to