## Is busy beaver the fastest growing function?

These Turing machines are called busy beavers. However, it is computable by an oracle Turing machine with an oracle for the halting problem. It is one of the fastest-growing functions ever arising out of professional mathematics.

### Is the busy beaver function computable?

The busy beaver function Σ The busy beaver function quantifies the maximum score attainable by a Busy Beaver on a given measure. This is a noncomputable function. Also, a busy beaver function can be shown to grow faster asymptotically than any computable function.

#### Why is busy beaver Uncomputable?

(BB(n) is defined as the number of steps made by n-state Busy Beavers.) Theorem: BB(n) is uncomputable. That is, there is no Turing machine that can take as input n and computes BB(n).

Why are beavers called Busy?

With powerful jaws and strong teeth, they fell trees in order to build homes and dams, often changing their environment in ways few other animals can. In fact, the idioms “busy as a beaver” and “eager beaver” are synonymous with being industrious and hardworking.

What is the fastest function?

There is no such thing as “the fastest growing function”. In fact, there is even no sequence of fastest growing functions. This was already shown by Hausdorff. Given two functions f,g:N⟶N, say that g grows faster than f if limn→∞g(n)f(n)=∞.

## Does Busy Beaver sell lumber?

Your Neighborhood Home Improvement Center! Featuring Lawn & Garden, Paint, Tools & Hardware, Lumber, Building Materials, Electrical, P. Busy Beaver is a full-line Home Improvement Center and …

### How many busy beaver stores are there?

16 stores
Currently, Busy Beaver operates 16 stores in three states, Pennsylvania, Ohio and West Virginia; and employs more than 270 people.

#### Is the Busy Beaver problem Undecidable?

The Busy Beaver numbers are an undecidable set; if they were decidable, we could figure out BB(n) for each n, enabling us to decide the halting problem. They are also not recursively enumerable, but for a trickier reason.

Is Busy beaver a saying?

(as) busy as a beaver (building a new dam) Very busy, assiduous, or hardworking. The phrase refers to beavers’ reputation for being extremely industrious. Between working two part-time jobs, volunteering on the weekends, and looking after his little brother, Sam’s been busy as a beaver this summer.

What is busy as a beaver?

Hardworking, very industrious, as in With all her activities, Sue is always busy as a bee, or Bob’s busy as a beaver trying to finish painting before it rains. The comparison to beavers dates from the late 1700s, the variant from the late 1300s. Also see eager beaver; work like a beaver.

## Which grows faster fingernails or toenails?

Your toenails grow much slower than your fingernails. They grow at an average rate of 1.62 mm per month. That’s three times as long as it would take your fingernail to regrow. This is because your toenails are generally subjected to less trauma than your fingernails.

### Which functions increase faster?

It is often important to determine how fast functions f(x) grow for very large values of x, and to compare the growth rate of various functions. Ex 1: Any quadratic function grows faster than any lin- ear function eventually. In fact, as x → ∞, the functions 2x and ex grow faster than any power of x, even x1,000,000.

#### Is the busy beaver function a computable function?

Radó showed that this function eventually dominates all computable functions, and thus it is uncomputable. That is, no algorithm that terminates after a finite number of steps can compute Σ(n) for arbitrary n. However, it is computable by an oracle Turing machine with an oracle for the halting problem.

Which is the solution to the busy beaver problem?

Let’s denote B (n) to be the number of 1s that the busy beaver managed to put on the tape. This function B (n) is called the busy beaver function and it is the solution to the busy beaver problem. The busy beaver function is also interesting – it grows faster than any computable function. It grows like this:

What is the maximum score of busy beaver?

The busy beaver function, Σ: N → N, is defined such that Σ(n) is the maximum attainable score (the maximum number of 1s finally on the tape) among all halting 2-symbol n-state Turing machines of the above-described type, when started on a blank tape.

## What is the purpose of the busy beaver game?

In theoretical computer science, the busy beaver game aims at finding a terminating program of a given size that produces the most output possible. Since an endlessly looping program producing infinite output is easily conceived, such programs are excluded from the game.