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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.
Busy Beavers is an online children's edutainment program. It is aimed at parents and teachers of toddlers who speak English or are learning English as a second language, and parents of children with a learning disability, autism or delayed speech. The Busy Beavers YouTube channel and website provide interactive media to help teach children ...
His work focused on computer science in the last decade of his life and in May 1962 he published one of his most famous results in the Bell System Technical Journal: the busy beaver function and its non-computability ("On Non-Computable Functions"). He died in New Smyrna Beach, Florida.
Busy beaver is an English language idiom describing of a person who is particularly busy or industrious. Busy beaver and related terms may also refer to: The Busy Beaver game, in computational theory, a type of Turing machine; Busy Beavers, an online children's educational program; The Busy Beavers, a 1931 Silly Symphonies animated film; Busy ...
As there is a recursive formula to define it, it is much smaller than typical busy beaver numbers, the latter of which grow 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.
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:
The Busy Beaver Game consists of desiging a halting, binary-alphabet Turing Machine which writes the most 1s on the tape, using only a limited set of states. The rules for the 2-state game are as follows: (i) the machine must have two states in addition to the halting state, and (ii) the tape starts with 0s only.