Busy Beaver Turing Machines It's easy to make a machine print an infinite # of 1's on its tape: s1 _ 1 R s1 But what about for a machine that halts? How many 1's can it print? Answer: it all depends on how many internal states the machine has. ;-------------------------- ; 1-state busy beaver ; INPUT: blank tape ; 1 step (not counting initial 0 -> s1 step), 1 one 0 * * * s1 s1 _ 1 R halt ;-------------------------- ; 2-state busy beaver ; INPUT: blank tape ; 6 steps, 4 ones 0 * * * s1 s1 _ 1 R s2 s1 1 1 L s2 s2 _ 1 L s1 s2 1 1 R halt ;-------------------------- ; 3-state busy beaver ; INPUT: blank tape ; 13 steps, 6 ones 0 * * * s1 s1 _ 1 R s2 s1 1 1 L s3 s2 _ 1 L s1 s2 1 1 R s2 s3 _ 1 L s2 s3 1 1 R halt ;-------------------------- ; 4-state busy beaver ; INPUT: blank tape ; 107 steps, 13 ones 0 * * * s1 s1 _ 1 R s2 s1 1 1 L s2 s2 _ 1 L s1 s2 1 _ L s3 s3 _ 1 R halt s3 1 1 L s4 s4 _ 1 R s4 s4 1 _ R s1 ;-------------------------- ; 5-state busy beaver (5a) ; INPUT: blank tape ; 134468 steps, 501 ones 0 * * * s1 s1 _ 1 R s2 s1 1 _ L s3 s2 _ 1 R s3 s2 1 1 R s4 s3 _ 1 L s1 s3 1 _ R s2 s4 _ _ R s5 s4 1 1 R halt s5 _ 1 L s3 s5 1 1 R s1 ;-------------------------- ; 5-state busy beaver (5b) ; INPUT: blank tape ; 11798827 steps, 4098 ones 0 * * * s1 s1 _ 1 R s2 s1 1 1 R s1 s2 _ 1 L s3 s2 1 1 L s2 s3 _ 1 R s1 s3 1 1 L s4 s4 _ 1 R s1 s4 1 1 L s5 s5 _ 1 L halt s5 1 _ L s3 ;-------------------------- ; 5-state busy beaver (5c) ; INPUT: blank tape ; 23554765 steps, 4097 ones 0 * * * s1 s1 _ 1 R s2 s1 1 _ L s4 s2 _ 1 L s3 s2 1 1 R s4 s3 _ 1 L s1 s3 1 1 L s3 s4 _ 1 R halt s4 1 1 R s5 s5 _ 1 R s1 s5 1 _ R s2 ;-------------------------- ; 5-state busy beaver (5d) ; INPUT: blank tape ; 47176871 steps, 4098 ones 0 * * * s1 s1 _ 1 L s2 s1 1 1 R s3 s2 _ 1 L s3 s2 1 1 L s2 s3 _ 1 L s4 s3 1 _ R s5 s4 _ 1 R s1 s4 1 1 R s4 s5 _ 1 L halt s5 1 _ R s1 ;-------------------------- ; 6-state busy beaver ; INPUT: blank tape ; more than 10^36534 steps ; more than 10^18267 ones 0 * * * s1 s1 _ 1 R s2 s1 1 1 L s5 s2 _ 1 R s3 s2 1 1 R s6 s3 _ 1 L s4 s3 1 _ R s2 s4 _ 1 R s5 s4 1 _ L s3 s5 _ 1 L s1 s5 1 _ R s4 s6 _ 1 L halt s6 1 1 R s3 ;--------------------------