On Wed, Aug 22, 2018 at 8:26 PM, <agrayson2...@gmail.com> wrote: >> >> Yes, the Busy Beaver Function is not computable. We know that: >> >> BB(1) =1 >> BB(2) =6 >> BB(3) =21 >> BB(4) =107 >> > > *>You haven't *written* the function, just its alleged values for > 1,2,3,4. What is the function? * >
Starting with a all zero tape BB(N) is the number of operations any N state Turing Machine performs after it writes the largest number of 1's and then halts. It is very important that it halt, some machines will go on forever but they don't count. For example we know for sure that BB(5) is at least 47,176,870 because one 5 state Turing Machine has been found that halts after it goes through 47,176,870 operations (and prints 4098 1’s on the tape), but there are 28 other 5 state machines displaying non-regular behavior that are well past 47,176,870 operations and 4098 1's. If one of them eventually halts then that larger number of operations will be BB(5), if none of them ever halts then 47,176,870 really is BB(5); but the trouble is we'll never be able to know it’s 47,176,870 because we'll never know that none of those other 28 5 state machines will never halt because the Halting problem is insolvable. John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
