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) Mathematics 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 http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
