I think you miss the difference between UTM, Universal turing machine and turing machine...
https://cs.stackexchange.com/questions/69197/difference-between-turing-machine-and-universal-turing-machine#:~:text=A%20Turing%20machine%20can%20be,input%20and%20generates%20some%20output . Le dim. 14 juil. 2024, 14:40, John Clark <[email protected]> a écrit : > On Sat, Jul 13, 2024 at 10:34 PM Brent Meeker <[email protected]> > wrote: > > *> The machine is universal. You don't need a different machine with >> different internal states.* > > > *First of all, the very definition of "a different Turing Machine" is > a machine with a different set of internal states*. And there is not just > one Turing machine, there are an *infinite* number of them. *There are > 64 one state two symbol (zero and one) Turing Machines, 20,736 two state, > **16,777,216 > three state, **25,600,000,000 four state, and **634,033,809,653,824 five > state two symbol T**uring Machines. * > > A Turing Machine with different sets of* internal states** will exhibit** > different > behavior even if given identical input states. *I think What confuses you > is that it is possible to have a machine in which the tape not only > provides the program the machine should work on but also the set of > internal states that the machine has. In a way you could think of the tape > as providing not only the program but also the wiring diagram of the > computer. A universal Turing Machine is in an undefined state until the > input tape, *or something else*, puts it in one specific state. > > *Consider the Busy beaver function, if you feed in a tape with all zeros > on it into all 4 state Turing Machines and ask "which of those > 25,600,000,000 machines will print the most ones before stopping" (it's > important that the machine eventually stops), you will find this is not an > easy question. All the machines are operating on identical input tapes (all > zeros) but they behave differently, some stop almost immediately, others > just keep printing 1 forever, but for others the behavior is vastly more > complicated. It turns out that the winner is a set of states that prints > out 13 ones after making 107 moves. * > > *A five state Turing Machine behaves differently, we just found out that a > particular set of internal states prints 2098 ones after making 47,176,870 > moves. I wouldn't be surprised if the sixth Busy Beaver number is not > computable, we know for a fact that any busy beaver number for a 745 State > Turing machine or larger is not computable. Right now all we know about > BB(6) is that it's larger than > 10^10^10^10^10^10^10^10^10^10^10^10^10^10^10.* > > *The point of all this is that Turing Machines with different sets of > internal states behave very differently. * > > John K Clark See what's on my new list at Extropolis > <https://groups.google.com/g/extropolis> > mth > > > > > >> -- > 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 [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAJPayv1NX6MaOW7eJo1TVbmpAfvb7k4CgvnYOGV%3DzfDt%2BpOo1w%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAJPayv1NX6MaOW7eJo1TVbmpAfvb7k4CgvnYOGV%3DzfDt%2BpOo1w%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAMW2kAqVhLgRBZPTfXj5CUcdEeQZUQr91dmfy-90vNxbwqrG8g%40mail.gmail.com.
