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Concept in theoretical computer science
In theoretical computer science, the busy beaver game aims to find a terminating program of a given size that (depending on definition) either produces
Busy_beaver
Topics referred to by the same term
Look up busy beaver in Wiktionary, the free dictionary. Busy beaver is an English language idiom describing of a person who is particularly busy or industrious
Busy_beaver_(disambiguation)
Turing machine on a two-dimensional grid
triangular grid, finding several busy beavers here too. Ed Pegg, Jr. considered another approach to the busy beaver game. He suggested turmites that can
Turmite
Turing table of instructions was derived from Peterson: "a three-state busy beaver writes 6 ones before it comes to a halt". Peterson moves the head; in
Turing_machine_examples
Computation model defining an abstract machine
{\displaystyle \{L,R\}} . The 7-tuple for the 3-state busy beaver looks like this (see more about this busy beaver at Turing machine examples): Q = { A , B , C
Turing_machine
1931 film
The Busy Beavers is a 1931 Silly Symphonies animated short film, produced by Walt Disney and directed by Burt Gillett. The short shows a community of beavers
The_Busy_Beavers
Abstract calculator
extra instructions. In the 2-state Busy Beaver example that we use only { J1xxx, Jxxx }. The mission of the busy beaver is to print as many ones as possible
Post–Turing_machine
Online children's educational program
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
Busy_Beavers
Proof assistant
proof using Rocq was completed in September 2012. Busy beaver: The value of the 5-state winning busy beaver was discovered by Heiner Marxen and Jürgen Buntrock
Rocq
Open problem on 3x+1 and x/2 functions
"Busy beaver competition and Collatz-like problems". Archive for Mathematical Logic. 32 (5): 351–367. doi:10.1007/BF01409968. "Hardness of busy beaver
Collatz_conjecture
Former steel company based in Pittsburgh, Pennsylvania, United States
Knoell, Cyclops purchased the Clairton, Pennsylvania based 16-chain Busy Beaver lumber stores in 1972, and the Silo Electronic Stores in 1980 for $35
Cyclops_Steel
Species of dam-building rodent
The North American beaver (Castor canadensis) is one of two extant beaver species, along with the Eurasian beaver (Castor fiber). It is native to North
North_American_beaver
Large number coined by Ronald Graham
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
Graham's_number
Problem in computer science
Minsky, T. Rado) and various technical papers. See note under Busy-Beaver Programs. Busy Beaver Programs are described in Scientific American, August 1984
Halting_problem
Domestic cat with distinctive coat markings
the original on 22 March 2019. Retrieved 6 March 2017. "I Met Morris | Busy Beaver Button Museum". ButtonMuseum.org. Archived from the original on 27 June
Tabby_cat
Malicious archive file designed to disrupt the program or system reading it
165 MB. Billion laughs attack, a similar attack on XML parsers Black fax Busy beaver, a program that produces the maximum possible output before terminating
Zip_bomb
Topics referred to by the same term
Europe Branch and bound, a method for solving optimization problems Busy beaver class in computing theory, a type of Turing Machine Beta blocker, medication
BB
Natural number
a Mersenne prime. 107 is itself a safe prime. It is the fourth Busy beaver number, the maximum number of steps that any Turing machine with 2 symbols
107_(number)
Numbers significantly larger than those used regularly
n's) fω2(n) = fωn(n) > (n → n → ... → n → n) (Chain of n+1 n's) The busy beaver function Σ is an example of a function which grows faster than any computable
Large_numbers
Any type of calculation
characterisation under this definition. This includes the halting problem and the busy beaver game. It remains an open question as to whether there exists a more powerful
Computation
Topics referred to by the same term
sigma function, related to elliptic functions Rado's sigma function, see busy beaver See also sigmoid function. This disambiguation page lists mathematics
Sigma_function
Eighteenth letter of the Greek alphabet
a system parameter. In theoretical computer science, Σ serves as the busy beaver function. In civil engineering, σ refers to the normal stress applied
Sigma
Belgian businessman
with the new Belgian company Lafig S.A. "The Snorks". buttonmuseum.org. Busy Beaver Button Museum. Retrieved 7 June 2020. "From The Scoop: The Snorks". diamondcomics
Freddy_Monnickendam
Dutch computer scientist
expressions. Tromp has done research on a lambda calculus-equivalent to the busy beaver function. Shotwell, Peter (2016). "John Tromp and the Big Numbers of
John_Tromp
Measure of algorithmic complexity
all large n {\displaystyle n} , where B B {\displaystyle BB} is the Busy Beaver shift function (also denoted as S ( n ) {\displaystyle S(n)} ). By modifying
Kolmogorov_complexity
Even integers as sums of two primes
to study computational complexity. The connection is made through the Busy Beaver function, where BB(n) is the maximum number of steps taken by any n state
Goldbach's_conjecture
Semiaquatic rodent
Beavers (genus Castor) are large semiaquatic rodents of the Northern Hemisphere. There are two extant species: the North American beaver (Castor canadensis)
Beaver
Hungarian mathematician (1895–1965)
of his most famous results in the Bell System Technical Journal: the busy beaver function and its non-computability ("On Non-Computable Functions"). He
Tibor_Radó
Topics referred to by the same term
Look up beaver in Wiktionary, the free dictionary. The beaver is a large semiaquatic rodent. Beaver or The Beaver may also refer to: Beaver Cleaver, in
Beaver_(disambiguation)
American computer scientist (born 1981)
widely distributed in academic computer science, uses the concept of Busy Beaver Numbers as described by Tibor Radó to illustrate the limits of computability
Scott_Aaronson
Topics referred to by the same term
in number theory σ Sigma-algebra (σ-algebra, σ-field) in set theory A busy beaver function in computability theory Σ Σ n 0 {\displaystyle \Sigma _{n}^{0}}
Sigma_(disambiguation)
Thesis on the nature of computability
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
Church–Turing_thesis
Regular expression denial-of-service attack
attack Billion laughs attack, a similar attack on XML parsers Black fax Busy beaver, a program that produces the maximum possible output before terminating
ReDoS
set of degrees of size less than continuum. Numerical values of the busy beaver function are known to be independent of ZFC, such as BB(748). This is
List of statements independent of ZFC
List_of_statements_independent_of_ZFC
American restaurant chain
Member Blue". Busy Beaver Button Museum. Archived from the original on June 3, 2018. Retrieved June 3, 2018. "National Big Boy Club". Busy Beaver Button Museum
Big_Boy_Restaurants
Self-referential paradox
we know that such computation is not possible because of the paradox. Busy beaver – Concept in theoretical computer science Definable real number – Real
Berry_paradox
Mathematical function that can be computed by a program
segment of an uncomputable sequence of natural numbers (such as the Busy Beaver function Σ) is computable. E.g., for each natural number n, there exists
Computable_function
Interactive theorem prover software
Magazine. Retrieved 2023-12-07. "We have proved "BB(5) = 47,176,870"". The Busy Beaver Challenge. 2024-07-02. Retrieved 2024-07-09. Barendregt, Henk; Geuvers
Proof_assistant
Study of computable functions and Turing degrees
Mathematics. North-Holland. ISBN 0-7204-2285-X. Aaronson, Scott (2025-06-28). "BusyBeaver(6) is really quite large". Shtetl-Optimized. Retrieved 2025-08-05. Radó
Computability_theory
Toffee candy bar from The Hershey Company
in the May 10, 1918 Confectioners Gazette (p. 20) "Fenn's Ice Cream | Busy Beaver Button Museum". buttonmuseum.org. "Heath Bar - Snack History". Snack
Heath_bar
Author of children's picture books
Tip-Tapping Toes by Carolyn Crimi. Booklist Online. Reviews of Get Busy, Beaver! Get Busy, Beaver!. Kirkus Reviews. Reviews of Boris and Bella Boris and Bella
Carolyn_Crimi
Natural number
partially ordered set with 11 unlabeled elements 47,176,870 = Fifth busy beaver number 47,326,700 = First number of the first consecutive centuries each
10,000,000
Character from American folklore
Macaulay company Fischer, Marjorie (November 29, 1953). Busy Beaver; The Remarkable Story of Tony Beaver, Montana. (review). New York Times "A Catalogue of
Tony_Beaver
Method of notation of very large integers
contexts. There exist functions which grow uncomputably fast, such as the Busy Beaver, which by their very nature will be completely out of reach from any
Knuth's_up-arrow_notation
Symbolic description of a mathematical object
characterisation under this definition. This includes the halting problem and the busy beaver game. It remains an open question as to whether there exists a more powerful
Expression_(mathematics)
(computer science) Art gallery theorem (geometry) Determination of the fifth Busy Beaver value (computer science) CAP theorem (theoretical computer science)
List_of_theorems
Election object worn as political advertising
Campaign buttons at Wikimedia Commons U.S. patent 401,094 Campaign Button, Patented 9 April 1889 Political Buttons from the Busy Beaver Button Museum
Campaign_button
Ornament or badge for wearing, as on a lapel, often with a slogan or image
2025-12-15. Wikimedia Commons has media related to Pin buttons. The Busy Beaver Button Museum Collection of United States Social Pinback Buttons. Yale
Pin-back_button
Sideshow performer (1844–1924)
From the collection of Lon Ellis. by christen@busybeaver.net for the Busy Beaver Button Museum Fan Museum". buttonmuseum.org. Retrieved 2026-07-09. Nickell
Eli_Bowen
Set with algorithmic membership test
homeomorphic finite simplicial complexes is not computable. The set of busy beaver champions is not computable. Hilbert's tenth problem is not computable
Computable_set
Beaver dam enlargement The beaver is a keystone species, increasing biodiversity in its territory through creation of ponds and wetlands. As wetlands
Environmental impacts of beavers
Environmental_impacts_of_beavers
Computational problems no algorithm can solve
every starting configuration). Determining whether a Turing machine is a busy beaver champion (i.e., is the longest-running among halting Turing machines
List_of_undecidable_problems
Technology for creating optical illusions
BaseballCardPedia.com". baseballcardpedia.com. "Pictorial Productions Inc. - Busy Beaver Button Museum". www.buttonmuseum.org. "Billboard". Nielsen Business Media
Lenticular_printing
Natural number
exactly 13 factors, a superperfect number 4098 – the fifth maximum-score busy beaver number 4104 = 23 + 163 = 93 + 153 4127 – safe prime 4133 – super-prime
4000_(number)
1965 film by John Sturges
a number of years… and, in spite of all predictions, shaggy hair and busy beaver to the contrary, the winter of eighteen sixty-seven turned out to be
The_Hallelujah_Trail
1976 graffiti mural
Harvard Crimson". www.thecrimson.com. "People's Bicentennial Commission | Busy Beaver Button Museum". www.buttonmuseum.org. "The Freedom Train @ 149st". www
The_Freedom_Train_(graffiti)
Doug, Judy, and Dirtbike's father who works as a photographer for the Busy Beaver department store. He quit to start his own studio toward the end of the
List_of_Doug_characters
Function that disables software after a particular date
resources. Billion laughs attack, a similar attack on XML parsers Black fax Busy beaver, a program that produces the maximum possible output before terminating
Time_bomb_(software)
Topics referred to by the same term
a pre-dreadnought battleship BB(5), notation representing the fifth busy beaver This disambiguation page lists articles associated with the same title
BB5
1988 film by Stephen Low
Vancouver, British Columbia. "Beavers". IMAX Victoria. Strickler, Jeff (24 January 1989). "Omnitheater film captures busy beavers' personalities, love for
Beavers_(film)
Type of abstract computing machine
One-instruction set computer Algorithm Algorithm characterizations Halting problem Busy beaver Stack machine WDR paper computer Background texts: The following bibliography
Register_machine
British button-badge manufacturer
Guardian. In September 2018 the Image as Virus exhibit went on show at the Busy Beaver Button Museum in Chicago. 1980 article in The Face -Pt.1 |Pt.2 |Pt.3
Better_Badges
Chocolate-coated toffee
Bar Boxes eBay via archive.org Big Bogie Candy Bar Wrapper (Circa 1940) eBay via archive.org "Fenn's Ice Cream Name Tag". Busy Beaver Button Museum.
Butter_Brickle
Former railroad union in the USA
VIRGINIA ex rel. VIRGINIA STATE BAR". Brotherhood Railroad Trainmen: Busy Beaver. History of the UTU ... UTU. United Transportation Union: Case Western
Brotherhood of Railroad Trainmen
Brotherhood_of_Railroad_Trainmen
Canadian/French animated children's television series
The Busy World of Richard Scarry is an animated children's television series, produced by CINAR Films and France Animation in association with Paramount
The Busy World of Richard Scarry
The_Busy_World_of_Richard_Scarry
Subfield of mathematics
by Pyotr Novikov in 1955 and independently by W. Boone in 1959. The busy beaver problem, developed by Tibor Radó in 1962, is another well-known example
Mathematical_logic
Children's animated television series
beach supposedly covered in petroglyphs, all they see is water. 31 31 "Busy Beavers" Uwe Rafael Braun Brian Clark Lazarino Baarde Sherwin Macario Alex Basio
Molly_of_Denali
"Bobcat Invasion" April 15, 2009 (2009-04-15) 12 12 "Extreme Roaches / Busy Beaver" April 22, 2009 (2009-04-22) 13 13 "Skunks and Mice and Snakes Oh My"
List of Billy the Exterminator episodes
List_of_Billy_the_Exterminator_episodes
to love God. The Beaver Scouts motto is "Busy and Bright". Dear Lord, help me to be a good Beaver, always busy and bright. Be with those so dear to me
Beaver Scouts (Baden-Powell Scouts' Association)
Beaver_Scouts_(Baden-Powell_Scouts'_Association)
of the Milky Way are discovered – Sextans II and Virgo III. The fifth busy beaver is proven. 5 July – The first mouse model with a complete, functional
2024_in_science
1980s political party in the US
Citizens Party of the United States (2011–present) "Citizens' Party 1980". Busy Beaver Button Museum. 2008. Retrieved January 16, 2025. Their platform covered
Citizens Party (United States)
Citizens_Party_(United_States)
American animated film series
China Plate May 23, 1931 Wilfred Jackson Frank Churchill 7:32 19 The Busy Beavers June 30, 1931 Burt Gillett 7:07 20 The Cat's Out July 28, 1931 Wilfred
Silly_Symphony
13 "Mickey Mouse in Black and White, Volume Two" Silly Symphonies The Busy Beavers Burt Gillett June 30 "Silly Symphonies" Mickey Mouse Mickey Steps Out
Walt Disney Productions short films (1928–1939)
Walt_Disney_Productions_short_films_(1928–1939)
Family of cellular automata to model feeding behaviour
different paths, and 209 of these are produced by just one species. Busy beaver – Concept in theoretical computer science Langton's ant – Two-dimensional
Paterson's_worms
Walt Disney DVD collection
Practical Pig (1939) The Ugly Duckling (1931) Birds of a Feather (1931) The Busy Beavers (1931) Just Dogs (1932) Father Noah's Ark (1933) Peculiar Penguins (1934)
Walt Disney Treasures: Wave One
Walt_Disney_Treasures:_Wave_One
American labor leader (1906–1992)
Profile of the month: W.P. Kennedy, p. 276. Brotherhood Railroad Trainmen: Busy Beaver. History of the UTU ... UTU. United Transportation Union: Case Western
Charles_Luna
Season of television series
The fourth season of the American television situation comedy Leave It to Beaver premiered on October 1, 1960 and concluded on June 24, 1961. It consisted
Leave_It_to_Beaver_season_4
American cabaret trio
queermusicheritage.com. Retrieved 2025-06-09. "Void Where Inhibited — MU0538 | Busy Beaver Button Museum". buttonmuseum.org. Retrieved 2025-06-03. Alan Eichler
Gotham_(band)
Military unit
Carter, Christen. "Kelllogg's [sic] Pep 370th Bombardment Squadron". Busy Beaver Button Museum. Retrieved 17 July 2026. This article incorporates public
370th_Flight_Test_Squadron
Series published in Boys' Life magazine
[Sailor] (wood) June: Cannibal (wood) July: Hound Dog (bone) August: Busy Beaver (wood) September: N.W. Coast Totem (wood) October: Old-Oil Lantern (wood)
Slide_of_the_Month
2007 Irish comedy television series
About Dan" After attending an enneagram personality assessment course 'Busy Beaver' Becs begins to question her compatibility with 'Lazy Bear' Dan. 4 "Free
Dan_&_Becs
Electronics retailer
the steel business and had already made one retail acquisition, the Busy Beaver home store chain in Pittsburgh, Pennsylvania. Cyclops was willing to
Silo_(store)
Chess variant with opposing armies of different composition
Colorbound Clobberers, including the weakening of the Bede to a piece named Busy Beaver, where the Dabbaba jump is replaced by a zigzag sliding move to the same
Chess_with_different_armies
1976 IMAX film by MacGillivray Freeman Films
November 19, 2021. "National Air and Space Museum To Fly". Chicago: Busy Beaver Button Museum. Archived from the original on February 28, 2021. Retrieved
To_Fly!
1972 studio album by David Peel & The Lower East Side
at 74". The New York Times – via NYTimes.com. "The Pope Smokes Dope – Busy Beaver Button Museum". www.buttonmuseum.org. "David Peel & the Lower East Side
The_Pope_Smokes_Dope
3rd episode of the 2nd season of Veronica Mars
to go through them. While Veronica is busy Beaver sees the photos taken while Kendall was meeting Logan. Beaver suddenly disappears and leaves the pictures
Cheatty_Cheatty_Bang_Bang
(complexity) Amortized analysis Arthur–Merlin protocol Best and worst cases Busy beaver Circuit complexity Constructible function Cook-Levin theorem Exponential
List of computability and complexity topics
List_of_computability_and_complexity_topics
Canadian literary award
Springett Isobel Springett Kate and Pippin Winner Nicholas Oldland The Busy Beaver Finalist Rebecca Bender Don't Laugh at a Giraffe Cary Fagan Geneviève
Blue_Spruce_Award
American cartoonist (1911–2003)
Anthony Strobl (Whitman, 1968; as Nick Tall) Woody Woodpecker and the Busy Beavers (Whitman, 1968; as Nick Tall) Mystery of the Coughing Dragon (Alfred
Kin_Platt
Park in Calgary, Alberta
Ring Road. Retrieved 1 March 2024. Kost, Hannah (17 November 2020). "Busy beavers chew down trees in Weaselhead Flats for new dam, winter prep". CBC. Retrieved
Weaselhead Flats Natural Environment Park
Weaselhead_Flats_Natural_Environment_Park
Racing car model
We may not have reached the end of the year yet, but we're already busy beavering away on the MCL37. "McLaren announce name for 2023 F1 car – and it's
McLaren_MCL60
Plateau", "Subharmonic Functions", in the Bell System Technical Journal the Busy Beaver problem received a doctorate from the university (1923) Frigyes Riesz
List of University of Szeged people
List_of_University_of_Szeged_people
Military unit
vehicle training Part of Air Education and Training Command Nicknames Busy Beaver Bombing Co. (CBI Theater), Fightin' Bees Engagements World War I Theater
492nd_Attack_Squadron
Symphonies Birds of a Feather Mother Goose Melodies The China Plate The Busy Beavers The Cat's Out Egyptian Melodies The Clock Store The Spider and the Fly
1931_in_film
Season of television series
The fifth season of the American television series Leave It to Beaver aired from September 30, 1961 to June 30, 1962 on ABC. It consisted of 39 black-and-white
Leave_It_to_Beaver_season_5
Traditional Animation The Bum Bandit United States Traditional Animation The Busy Beavers United States Traditional Animation By the Beautiful Sea United States
List of animated short films of the 1930s
List_of_animated_short_films_of_the_1930s
American film director (1891–1971)
Goose Melodies (1931) The Moose Hunt (1931) The Delivery Boy (1931) The Busy Beavers (1931) Mickey Steps Out (1931) Blue Rhythm (1931) Fishin' Around (1931)
Burt_Gillett
American baseball player (1911–1992)
California after a stroke at age 81. "Chicago Cubs Tuck Stainback | Busy Beaver Button Museum". www.buttonmuseum.org. Retrieved April 24, 2019. "Tuck
Tuck_Stainback
Boy Scout Council of western TX and OK
Badge and other youth training events. Nischa Achowalogen Lodge #486 Busy Beaver Cherokee Iron Horse Zulu Scouting in Texas Hook, James; Franck, Dave;
Golden_Spread_Council
Russian actor and singer (born 1949)
(2009) Order of Honour (Moldova) (2011) Order of Honour (2020) 2011 — Busy Beavers — Allagator Михаил Боярский завершает карьеру: что у актера со здоровьем
Mikhail_Boyarsky
travel, tourism, insurance
BUSY BEAVER
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BUSY BEAVER
travel, tourism, insurance