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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.
It is the fourth Busy beaver number, the maximum number of steps that any Turing machine with 2 symbols and 4 states can make before eventually halting. [4] It is the number of triangle-free graphs on 7 vertices. [5] It is the ninth emirp, because reversing its digits gives another prime number (701)
However, Graham's number can be explicitly given by computable recursive formulas using Knuth's up-arrow notation or equivalent, as was done by Ronald Graham, the number's namesake. 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 ...
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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:
In computability theory, a busy beaver is a Turing machine that attains the maximum number of steps performed, or maximum number of nonblank symbols finally on the tape, among all Turing machines in a certain class.
In 2015, Busy Beavers joined the Channel Frederator Network and is by views the number one channel of the multi-channel network. [4] In April 2016, Busy Beavers and Baby Beavers have both been added to Roku, [5] and Kidoodle.TV in September 2016. [6] They have also created an app for iOS called Busy Beavers Jukebox.
[36] [37] The connection is made through the Busy Beaver function, where BB(n) is the maximum number of steps taken by any n state Turing machine that halts. There is a 15 state Turing machine that halts if and only if a conjecture by Paul Erdős (closely related to the Collatz conjecture) is false. Hence if BB(15) was known, and this machine ...