In computability theory, a busy beaver (from the colloquial expression for an industrious person) is a Turing machine that attains the maximum "operational busyness" (such as measured by the number of steps performed, or the number of nonblank symbols finally on the tape) among all the Turing machines in a certain class. The Turing machines in this class must meet certain design specifications and are required to eventually halt after being started with a blank tape.
A busy beaver function quantifies these upper limits on a given type of "operational busyness", and is a noncomputable function. In fact, a busy beaver function can be shown to grow faster asymptotically than does any computable function. The concept was first introduced by Tibor Radó as the "busy beaver game" in his 1962 paper, "On Non-Computable Functions".
Read more about Busy Beaver: The Busy Beaver Game, The Busy Beaver Function Σ, Non-computability of Σ, Σ, Complexity and Unprovability, Max Shifts Function, Known Values, Generalizations, Applications, Proof For Uncomputability of S(n) and Σ(n), Examples of Busy Beaver Turing Machines, Exact Values and Lower Bounds For Some S(n, m) and Σ(n, m)
Famous quotes containing the words busy and/or beaver:
“These people who are always briskly doing something and as busy as waltzing mice, they have little, sharp, staccato ideas.... But they have no slow, big ideas. And the fewer consoling, noble, shining, free, jovial, magnanimous ideas that come, the more nervously and desperately they rush and run from office to office and up and downstairs, thinking by action at last to make life have some warmth and meaning.”
—Brenda Ueland (1891–1985)
“The mission of men there seems to be, like so many busy demons, to drive the forest all out of the country, from every solitary beaver swamp and mountain-side, as soon as possible.”
—Henry David Thoreau (1817–1862)