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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.
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.
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:
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:
Ed Pegg, Jr. considered another approach to the busy beaver game. He suggested turmites that can turn for example both left and right, splitting in two. Turmites that later meet annihilate each other. In this system, a Busy Beaver is one that from a starting pattern of a single turmite lasts the longest before all the turmites annihilate each ...
As there is a recursive formula to define it, it is much smaller than typical busy beaver numbers, the sequence of which grows faster than any computable sequence. Though too large to ever be computed in full, the sequence of digits of Graham's number can be computed explicitly via simple algorithms; the last 13 digits are ...7262464195387.
Beavers can stay underwater for up to 15 minutes at a time. When they're underwater, their noses and ears shut to keep water out. They also have transparent inner eyelids that close over each eye ...
Finding an upper bound on the busy beaver function is equivalent to solving the halting problem, a problem known to be unsolvable by Turing machines. Since the busy beaver function cannot be computed by Turing machines, the Church–Turing thesis states that this function cannot be effectively computed by any method.