BUSY BEAVER

Domain	Definition
Computing	Busy Beaver (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). Source: The Free On-line Dictionary of Computing.
Math	(1) A Turing machine with a small number of states which halts when started with a blank tape, but which writes a huge number of non-blanks or takes a huge number of steps. (2) The problem of finding the maximum number of non-blanks written or steps taken for any Turing machines with a given number of states and symbols. (references)
Source: compiled by the editor from various references; see credits.

Specialty Definition: Busy beaver

A busy beaver (from the colloquial expression for "industrious person") is a Turing machine that, when given an initially empty tape (a string of only 0's), does a lot of work, then halts. The functions defined below, called busy beaver functions, were introduced and their properties proved in 1952, by Tibor Rado. There are two main 'categories':

Sigma(n): the largest number of 1's printable by an n-state machine before halting, and
S(n): the largest number of steps taken by an n-state machine before halting.

All machines are started on initially blank tapes and those that do not halt are not candidates.

Both of these functions are uncomputable in general.

Even with only a few states, a Busy Beaver can do very much. At the moment the record 6-state Busy Beaver is over 10⁸⁶⁵ (that is a 1 with 865 zeros) ones produced, using over 10¹⁷³⁰ steps.

There is an analog to the Sigma function for Minsky machines, namely the largest number which can be present in any register on halting, for a given number of instructions. This is a consequence of the Church-Turing thesis.

External links:

The page of Heiner Marxen who with Jürgen Bontrock found the above mentioned record for a 6-state turing machine.

Anagrams: BUSY BEAVER

Scrabble® Enable2K-Verified Anagrams
	Words within the letters "a-b-b-e-e-r-s-u-v-y"
	-3 letters: baubees, beavers, eyebars, yabbers.
	-4 letters: abbeys, abuser, averse, barbes, baryes, baubee, beaver, braves, breves, bursae, busbar, buyers, eyebar, reaves, rebbes, rebuys, reseau, revues, suaver, survey, urease, yabber, yerbas.
	-5 letters: abbes, abbey, abuse, abyes, aures, avers, babes, babus, barbe, barbs, bares, barye, baser, bears, beaus, beers, beery, braes, brave, brays, brees, breve, buras, burbs.
Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro.