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An n-th busy beaver, BB-n or simply "busy beaver" is a Turing machine that wins the n-state busy beaver game. [5] Depending on definition, it either attains the highest score, or runs for the longest time, among all other possible n -state competing Turing machines.
The mission of the busy beaver is to print as many ones as possible before halting. The "Print" instruction writes a 1, the "Erase" instruction (not used in this example) writes a 0 (i.e. it is the same as P0). The tape moves "Left" or "Right" (i.e. the "head" is stationary). State table for a 2-state Turing-machine busy beaver:
The diagram "progress of the computation" shows the three-state busy beaver's "state" (instruction) progress through its computation from start to finish. On the far right is the Turing "complete configuration" (Kleene "situation", Hopcroft–Ullman "instantaneous description") at each step.
The "state" drawing of the 3-state busy beaver shows the internal sequences of events required to actually perform "the state". As noted above Turing (1937) makes it perfectly clear that this is the proper interpretation of the 5-tuples that describe the instruction. [1] For more about the atomization of Turing 5-tuples see Post–Turing machine:
"Direction" of a state transition is shown by an arrow. The label (e.g.. 0/P,R) near the outgoing state (at the "tail" of the arrow) specifies the scanned symbol that causes a particular transition (e.g. 0) followed by a slash /, followed by the subsequent "behaviors" of the machine, e.g. "P Print" then move tape "R Right".
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The Nth busy beaver or BB-n is the Turing Machine that wins the N-state Busy Beaver Game. That is, it attains the maximum number of 1s among all other possible N-state competing Turing Machines. The BB-2 turing machine, for instance, achieves four 1s in six steps.
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