busy beaver - meaning and definition. What is busy beaver
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What (who) is busy beaver - definition

A HALTING, BINARY-ALPHABET TURING MACHINE WHICH WRITES THE MOST 1S ON THE TAPE, USING ONLY A LIMITED SET OF STATES
Busy Beaver; Busy beaver function; Busy beaver problem; Busy Beaver function; Busy Beaver problem; Busy Beaver Problem; Busy Beaver Number; Maximum shifts function; Busy-beaver; N-state busy beaver game; BB-n game; Generalized busy beaver functions; Busy Beaver game
  • Animation of a 3-state, 2-symbol busy beaver
  • Animation of a 4-state, 2-symbol busy beaver
  • Shows the first 100,000 timesteps of the current best 5-state busy beaver. Orange is "1", white is "0" (image compressed vertically).

Busy Beaver         
<theory> (BB) One of a series of sets of Turing Machine programs. The BBs in the Nth set are programs of N states that produce a larger finite number of ones on an initially blank tape than any other program of N states. There is no program that, given input N, can deduce the productivity (number of ones output) of the BB of size N. The productivity of the BB of size 1 is 1. Some work has been done to figure out productivities of bigger Busy Beavers - the 7th is in the thousands. (1994-10-24)
Busy beaver (disambiguation)         
WIKIMEDIA DISAMBIGUATION PAGE
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:
Busy Beavers         
ONLINE CHILDREN'S EDUCATIONAL PROGRAM
Draft:Busy Beavers; We Are Busy Beavers; Billy Beaver; Betty Beaver; Busy Beavers TV; Busy Beavers Jukebox; Baby Beavers
Busy Beavers (also known as We Are Busy Beavers) is an online children's educational 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.

Wikipedia

Busy beaver

In theoretical computer science, the busy beaver game aims at finding a terminating program of a given size that produces the most output possible. Since an endlessly looping program producing infinite output is easily conceived, such programs are excluded from the game.

More precisely, the busy beaver game consists of designing a halting Turing machine with alphabet {0,1} which writes the most 1s on the tape, using only a given set of states. The rules for the 2-state game are as follows:

  1. the machine must have two states in addition to the halting state, and
  2. the tape initially contains 0s only.

A player should conceive a transition table aiming for the longest output of 1s on the tape while making sure the machine will halt eventually.

An nth busy beaver, BB-n or simply "busy beaver" is a Turing machine that wins the n-state Busy Beaver Game. That is, it attains the largest 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.

Determining whether an arbitrary Turing machine is a busy beaver is undecidable. This has implications in computability theory, the halting problem, and complexity theory. The concept was first introduced by Tibor Radó in his 1962 paper, "On Non-Computable Functions".