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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. [4] Depending on definition, it either attains the highest score (denoted by Σ(n) [ 3 ] ) , or runs for the longest time ( S(n)) , 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:
While every time the busy beaver machine "runs" it will always follow the same state-trajectory, this is not true for the "copy" machine that can be provided with variable input "parameters". The diagram "progress of the computation" shows the three-state busy beaver's "state" (instruction) progress through its computation from start to finish.
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The following is a test-case to see what it looks like. It will look better with Netscape viewer. You can find the 2-state 2-symbol busy beaver at Post-Turing machine and as mentioned in the article, the 3-state 2-symbol busy beaver at Turing machine examples. wvbaileyWvbailey 20:37, 22 August 2006 (UTC)