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Topic: Busy beaver

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	Busy Beaver
		A platypus is an Australian monotreme, and hence is native to the southern hemisphere (as the beaver is to the north).
		The busy beaver function may be thought of as seeking the maximum number of 1's that can be printed for a given number of states.
		Analagously to the busy beaver case, we also consider the minimum number of transitions required to print m 1's; we denote this function as the weary wombat, or ww(n), which is the minimum number of state transitions made by a terminating machine which prints n 1's.
	goanna.cs.rmit.edu.au /~jah/busybeaver (1229 words)

	Beaver Management
		Beaver parents are quite protective of their young, and the kits often stay with the parents for two years, after which they disperse to find their own territories.
		The beavers we see in the mainstem of the Chena River, which appears to be impossible to dam, are probably either dispersing young who have not yet found a territory, or adult males that have moved from their home lodges while kits are young.
		Beaver populations have rebounded throughout North America, and beavers often conflict with humans because their dams create ponds that flood roads and trees, and because they cut down and eat trees that humans prefer to be left standing.
	www.northstar.k12.ak.us /schools/awe/noyes/beaver.html (1478 words)

	Beaver: Wildlife Notebook Series - Alaska Department of Fish and Game
		The beaver's scientific name is descriptive of the castor glands which are located near the base of the tail.
		Beavers build canals to float and transport heavy objects such as branches and logs for food and construction.
		Occasionally beaver dams may block streams to migrating anadromous fish, like salmon, and at times road culverts may be blocked or other human developments flooded by this industrious animal.
	www.adfg.state.ak.us /pubs/notebook/furbear/beaver.php (937 words)

	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.
		At the moment the record 6-state Busy Beaver is over 10^865 (that is a 1 with 865 zeros) ones produced, using over 10^1730 steps.
		There is an analog to 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.
	www.ebroadcast.com.au /lookup/encyclopedia/bu/Busy_beaver.html (194 words)

	Good Math has moved to ScienceBlogs: Busy Beavers
		There are actually real competitions to see who can build the best busy beaver program.
		Here's the question that the simplest version of the busy beaver problem wants to answer: Given a binary turing machine (that is a machine whose tape can have only the characters 0 and 1) with N states, what is the longest string of 1s that can be generated by a halting program?
		There are numerous variations on the busy beaver problem: versions for turing machines with more symbols on the input tape; versions where the goal is to run for the most execution steps before halting; versions for other computing systems; etc.
	goodmath.blogspot.com /2006/05/busy-beavers.html (744 words)

	The Busy Beaver Problem : A NEW MILLENNIUM ATTACK
		Comprehension of the Busy Beaver problem requires a conceptual understanding of what a turing machine is and does.
		The definition of the Busy Beaver problem defined above makes no reference to the nature of the tape after the machine has halted beyond strictly the number of 1's that are present.
		A variant of the problem enforces the additional restriction that a machine can not be considered a Busy Beaver candidate unless the resulting pattern of 1's on the tape is in a contiguous sequence with the read head located at the left-most 1.
	www.cs.rpi.edu /~kelleo/busybeaver/problem.html (1285 words)

	Western New York Travel Guide: Beaver Meadow Nature Center
		Beavers were nearly extinct in the state at the turn of this century.
		Two beaver lodges, also built of sticks and poles, are located near the dam.
		The homes are used by the beaver family to rest during the day as well as throughout much of the winter.
	www.westernny.com /beaver.html (416 words)

	Regional home center chain Busy Beaver survives among national giants (Site not responding. Last check: 2007-10-21)
		Busy Beaver Building Centers last year found itself in a not all-that-unfamiliar position to smaller home center stores -- it lost money, ending a two-year string of record profits for the regional chain.
		Busy Beaver is surviving by playing its industry's version of small ball.
		Busy Beaver has spent the past several years trying to stay out of the big chains' way.
	www.post-gazette.com /pg/06136/690405-28.stm (991 words)

	Busy Beaver — American Executive Spotlight (Site not responding. Last check: 2007-10-21)
		Busy Beaver does not solicit business from contractors or professionals since it doesn’t want to spread itself too thin, he said.
		Busy Beaver now has a comprehensive point-of-sale system tied to an automated replenishment system.
		Bender said Busy Beaver cannot afford to be the first to buy all the technological advances as soon as they hit the shelves.
	www.redcoatpublishing.com /spotlights/sl_06_05_Busybeaver.asp (791 words)

	Busy beaver - Wikipedia, the free encyclopedia
		The n-state Busy Beaver (BB-n) game is a competition to find an n-state Turing machine which leaves the largest number of 1s on its tape before halting.
		The current 5-state 2-symbol Busy Beaver champion produces 4,098 1s, using 47,176,870 steps (Discovered by Heiner Marxen and Jürgen Buntrock in 1989), but there remain about 40 machines with nonregular behavior which are believed to never halt, but which have not yet been proven to run infinitely.
		Busy Beaver Programs are described by Alexander Dewdney in Scientific American, August 1984, pages 19-23, also March 1985 p.
	en.wikipedia.org /wiki/Busy_beaver (2699 words)

	Dahlen Marine Service \| Under Water Tree Cutting \| Under Water Tree Stump Removal
		Busy Beaver ™ works in most weather, in as little as 18 inches of water.
		The Busy Beaver ™ is an enviornmentally safe machine that does not require a Corps of Engineer's permit.
		The removal part of the obstruction is so collected by Busy Beaver ™ to be disposed of as you specify.
	www.dahlenmarineservice.com /index.htm (182 words)

	Home Page (Site not responding. Last check: 2007-10-21)
		Established in 1967, Busy Beaver, Inc. is a full service industrial flooring contractor that has the reputation for professionalism, integrity and reliability.
		Busy Beaver, Inc. provides the highest quality concrete floor protection in the business.
		At Busy Beaver, Inc., our mission is to be the preferred supplier of industrial floor care services, offering solutions that exceeds the expectations of our customers and result in total customer satisfaction.
	www.busybeaverinc.com (233 words)

	busy beaver (Site not responding. Last check: 2007-10-21)
		This problem is related to the halting problem since one must determine if a machine is looping or eventually halts.
		History, explanation, and links about the Busy Beaver Turing Machine.
		Paul E. Black, "busy beaver", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/busyBeaver.html (176 words)

	busy - Definitions from Dictionary.com
		Busy, diligent, industrious imply active or earnest effort to accomplish something, or a habitual attitude of such earnestness.
		Busy, the most general, sometimes indicates constant and customary work or activity: a busy lawyer; a busy day.
		actively or fully engaged or occupied; "busy with her work"; "a busy man"; "too busy to eat lunch"; "the line is busy" [ant: idle]
	dictionary.reference.com /browse/busy (628 words)

	Amazon.ca: Get Busy, Beaver!: Books: Carolyn Crimi,Janie Bynum (Site not responding. Last check: 2007-10-21)
		PreSchool-Grade 2–The Beavers are busy rebuilding their dam, except for Thelonious, who daydreams and idles the day away.
		While his family is working harder and harder to keep up with their neighbors, he creates an artistic structure of trees, leaves, and flowers inspired by his observations of the world around him.
		He's a little different.While Ma, Pa, and Babs Beaver hurry, hurry, hurry to make their dam bigger, bigger, bigger, Thelonious is busy with a project of his own -- a creation so beautiful that it changes everything.
	www.amazon.ca /Get-Busy-Beaver-Carolyn-Crimi/dp/0439548667 (395 words)

	Busy Beaver Turing Machine
		Uhing was looking for a particular Turing machine dubbed a "busy beaver," which satisfies the condition: If a Turing machine has five possible states, what is the largest number of ones it can print on a blank tape (all zeros to start with) before coming to a stop?
		It is now known that a three-state busy beaver writes six ones before it halts; a four-state busy beaver writes 13 ones.
		However, Uhing doesn't know yet whether his machine is the long-sought busy beaver because other five-state machines may exists that print out even more ones.
	grail.cba.csuohio.edu /~somos/busy.html (1319 words)

	Busy Beavers Build Piles Of Sticks
		The "busy beaver" has been used as a metaphor and a model for productive people for ages.
		It's worth noting that the beavers were very efficient at piling sticks on tape recorders.
		It's time to be an effective beaver instead of a busy beaver.
	www.alumbo.com /article/12743-Busy-Beavers-Build-Piles-Of-Sticks.html (439 words)

	Heiner Marxen - Attacking the Busy Beaver 5
		The busy beaver game as defined by T. Rado in 1962 [Rad62] asks to construct simple Turing machines which produce a maximum number of ones on their tape before halting.
		These Turing machines have N states, one of which is the initial state, a tape alphabet with two symbols, named 0 and 1, an initial tape with all 0 symbols, an anonymous halt state, and with each step print a new symbol and move their head either left or right.
		Busy beavers can be found without (4), computation of Sigma needs it.
	www.drb.insel.de /~heiner/BB/mabu90.html (2612 words)

	Heiner Marxen - Busy Beaver
		There is an interesting relation between non-halting proofs for busy beaver Turing Machines and The Superset Algorithm of M.Najtiv.
		You may read about their evolutionary approach to find busy beavers.
		Rick J. Griffiths in his dissertation in 2003 has adapted the busy beaver problem to Minsky's "register machines".
	www.drb.insel.de /~heiner/BB (1036 words)

	Busy Beaver (Site not responding. Last check: 2007-10-21)
		The Busy Beaver function was formulated and shown to be Turing-uncomputable by Tibor Rado in 1962.
		Finding these values creates interesting engineering challenges (how to find Busy Beavers in the vast space of all possible computer programs), and also raises fundamental philosophical questions (what are the theoretical boundaries of computation and demonstration?).
		To address these challenges and questions, the Busy Beaver Project: A New Milennium Attack was created as a multidisciplinary project between the departments of Cognitive Science and Computer Science.
	www.rpi.edu /~heuveb/research/BB/bb.html (246 words)

	www.myspace.com/busybeaver
		Busy Beaver Button Co Chicago, IL US mascot
		Busy Beaver Button Co is in your extended network
		Hi Busy Beaver, do you think they're lost.
	www.myspace.com /busybeaver (324 words)

	Genetic Beaver Project
		The Genetic Beaver is an ongoing research project, developed at CISUC's AI Lab.
		To assess this idea we selected, as test problem, the Busy Beaver Problem -- a well-known theoretical problem proposed by Tibor Rado in 1962, of undisputed interest and difficulty.
		Using the graph-based crossover operator, in conjunction with the new interpretation techniques, and with slight changes to the simulator of Turing Machines, we established new best candidates for the 6, 7, and 8 states instances of the 4-tuple Busy Beaver problem.
	eden.dei.uc.pt /~machado/research/bb/BB.html (1169 words)

	Busy Beaver--Language Arts: Grades 1-3 (Site not responding. Last check: 2007-10-21)
		Draw the students' attention to the beaver display created in the previous lesson.
		Ask if a beaver uses all of his tools at once, or one at a time.
		To review the tools, point to the beaver parts one at a time and ask students to name a convention to look for in editing.
	www.teachercreated.com /lessons/030131pl.shtml (381 words)

	Busy Beaver Problem of Tibor Rado ("Busy Beaver Game")
		In a stunning addition to known results in the Busy Beaver Game, Gregory Lafitte and Christophe Papazian have just announced discovery of a 3x3 (three state by three symbol) machine which brings the lower bound of S(3,3) up to 987,522,842,126 steps.
		Henceforth I shall use the term "Output Length" to describe the length of the output string from the leftmost nonblank symbol to the rightmost, inclusive.
		He has recently completed a paper about the Busy Beaver problem which relates the behavior of some of these (3,3) machines in particular to what he describes as "Collatz-like behavior" (paper in PDF format).
	www.cs.unr.edu /~al/BusyBeaver.html (3381 words)

	Busy Beaver Express Inc - Brandon, FL- Welcome
		Busy Beaver Express (aka "The Beav") takes the hassle out of getting your packages to your destinations.
		When business is booming, you and your employees don’t have time to traipse across town, fumbling with maps, searching for hidden address signs and making deliveries when you can be in the office being productive and making money.
		If your company has too much to do and not enough time to do it, Busy Beaver Express wants to be a part of your team.
	www.busybeaverexpress.com (366 words)

	Busy Little Beaver Plush & Book Set
		His mate is going to have her babies soon, and Beaver must build a strong, safe lodge for his new family.
		While chewing on a tasty tree, Beaver suddenly smells danger.
		Beaver runs, but the sly fox is right behind him.
	www.otterbaygifts.com /shop/singles/3990.htm (65 words)

	Busy beaver swam with dinosaurs - World - smh.com.au
		Despite similarities with some modern animals, the Jurassic mammal has no modern descendants and is not related to any existing species.
		The discoverers have given it the name Castorocauda lutrasimilis, Latin for beaver tail.
		Dr Zhe-Xi Luo, one of the discoverers, said the specimen was well preserved, unlike the fragments of bone and tooth that survive of most mammals from the dinosaur age.
	www.smh.com.au /news/world/busy-beaver-swam-with-dinosaurs/2006/02/24/1140670261970.html (608 words)

	Busy Beaver - June 14, 2006
		After all, the Oregon State University athletic director, who had just finished a round of 18 at the Beavers’ fundraising tournament, has witnessed on his watch one of the most successful spring seasons in Oregon State history.
		Coach Pat Casey and the eighth-ranked Beavers baseball squad will continue their postseason run on Saturday at the eight-team, double-elimination College World Series in Omaha, Neb. OSU opens with 24th-ranked Miami at 4 p.m.
		The Beavers made more news off the field when it was announced the Civil War game with the University of Oregon will be moved to a Friday (Nov. 24).
	www.mailtribune.com /archive/2006/0614/sport/stories/01sport.htm (574 words)

	Busy Beaver Problem (Site not responding. Last check: 2007-10-21)
		The Busy Beaver, BB, problem for Turing machines, TMs, was first posed by Rado in the early 1960's.
		Pascal Michel has a number of webpages devoted to the Busy Beaver problem with links on his homepage including Turing machines: an Introduction, The Busy Beaver Competitions, Histortical survey of Busy Beavers, and Behavior of busy beavers.
		Again, documentation and details of the current results (and histories) can be found on Pascal Michel's Histortical survey of Busy Beavers, and Heiner Marxen's Busy Beaver Simulations.
	seesar.lbl.gov /anag/staff/ligocki/MathMusing/BusyBeaver (455 words)

	Busy Beaver (Site not responding. Last check: 2007-10-21)
		In 1962 Rado introduced this "busy beaver competition." In more detail, the ground rules for the competition are as follows.
		In fact, if you want to start from scratch and construct a specific non-computable function, this is the one to use.
		Paper: Click here for a paper about the busy beaver problem.
	www.math.ucla.edu /~hbe/beaver.html (355 words)

	Busy Beaver problem (Site not responding. Last check: 2007-10-21)
		At present, their most productive seven-state (4-tuple) Busy Beaver candidate prints 164 *'s after 23,197 transitions.
		Most published work on the Busy Beaver problem has focussed on 5-tuple Turing machines (that is, Turing machines that both write a symbol and move at each state transition), rather than 4-tuple Turing machines (which either write or move, but not both, at each state transition).
		For example, using 5-tuple machines, a six-state Busy Beaver candidate has been found by J. Buntrock and H. Marxen that prints over 95 million *'s before halting--after 8 quadrillion (8 x 10^15) state transitions.
	www-csli.stanford.edu /hp/Beaver.html (301 words)

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