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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 "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:
Busy beaver: The value of the 5-state winning busy beaver was discovered by Heiner Marxen and Jürgen Buntrock in 1989, but only proved to be the winning fifth busy beaver — stylized as BB(5) — in 2024 using a proof in Coq.
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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Allen H. Brady searched for terminating turmites (the equivalent of busy beavers) and found a 2-state 2-color machine that printed 37 1's before halting, and another that took 121 steps before halting. [3] He also considered turmites that move on a triangular grid, finding several busy beavers here too.