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.

What’s the fastest growing function?

There is no fastest growing function: if grows with , then grows much more quickly. There are a bunch of functions that you can define that grow much more quickly than the factorial function. The simplest is , which outpaces the factorial but isn’t all that impressive.

Is Busy Beaver computable?

The busy beaver function BB(n) describes the maximum number of steps that an n-state Turing machine can execute before it halts (assuming it halts at all). It is not a computable function because computing it allows you to solve the halting problem.

Is tree a computable function?

Since TREE is a computable function the BB function grows faster than it, but TREE seems to grow much more quickly early on, so when does Busy Beaver surpass it?

Who can name the biggest number?

The largest number with a name (excluding ‘infinity’ which is not really a number) is the ‘googolplex’. The term googol was first coined in 1929 by Edward Kasner supposedly when he asked his nephew to give a name to the number 10 to the power of 100 (or 1 followed by 100 zeroes).

Which is the slowest growing function?

Well, there is no such thing as slowest, because given a slow function , the function , will be even slower. If you are looking for an extremely slow growing function, then the Inverse Ackermann function is a good candidate.

Do exponents or Factorials grow faster?

Factorials grow faster than exponential functions, but much more slowly than doubly exponential functions.

Is Busy Beaver NP complete?

An nth busy beaver, BB-n or simply “busy beaver” is a Turing machine that wins the n-state Busy Beaver Game. That is, it attains the largest number of 1s among all other possible n-state competing Turing Machines….Nondeterministic Turing machines.

p	steps	states
5	8	15
6	7	18
7	6	18

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.

Is TREE 4 bigger than TREE 3 ))?

In fact, they are probably so much bigger that even TREE(4) will dwarf TREE(3) to a much greater extent than TREE(3) dwarfs our familiar numbers. But that isn’t surprising once you know about TREE(3).

Is a busy beaver function faster than a computable function?

Also, a busy beaver function can be shown to grow faster asymptotically than any computable function.

What is a busy beaver Turing machine?

An nth busy beaver, BB-n or simply “busy beaver” is a Turing machine that wins the n-state Busy Beaver Game. That is, it attains the largest number of 1s among all other possible n-state competing Turing Machines.

What is the busy beaver game in Computer Science?

The Busy Beaver Game has implications in computability theory, the halting problem, and complexity theory. The concept was first introduced by Tibor Radó in his 1962 paper, “On Non-Computable Functions”.

Why is the busy beaver game excluded from the Turing test?

Since an endlessly looping program producing infinite output is easily conceived, such programs are excluded from the game. More precisely, the busy beaver game consists of designing a halting, binary-alphabet Turing machine which writes the most 1s on the tape, using only a given set of states.