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Why is busy beaver not computable?
1 A busy beaver is a TM that attains the maximum number of steps performed or number of non-blank symbols finally on the tape among all TMs in a certain class. A busy beaver function quantifies these upper limits on a given measure, and is a non-computable function.
Is busy beaver computable?
The busy beaver function Σ Also, a busy beaver function can be shown to grow faster asymptotically than any computable function. This infinite sequence Σ is the busy beaver function, and any n-state 2-symbol Turing machine M for which σ(M) = Σ(n) (i.e., which attains the maximum score) is called a busy beaver.
What’s the meaning of 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.
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.
What is the halting problem in computer science?
computers. … unsolvable algorithmic problem is the halting problem, which states that no program can be written that can predict whether or not any other program halts after a finite number of steps. The unsolvability of the halting problem has immediate practical bearing on software development.
Do beavers build dams?
What do beavers use to build their dams? Beavers build their dams out of trees and branches that they cut using their strong incisor (front) teeth! They also use grass, rocks, and mud.
Where does busy as a beaver come from?
This idiom is originated back in 1700. Since last few hundred years, beaver has been taken as a symbol of hard work and busyness. If you observe it, you’ll see how it works all day to cut trees with its teeth and to build dams. Therefore, this expression is used for those who always remain busy in their work.
How do you prove a number is normal?
We call a number normal if fk(w,n)→110 as n→∞ for k=1,2,3,4,5,6,7,8,9. Prove that 0.123456789101112… is normal. So the number of times 1 appear in the first 9 digits after the decimal point is 1, then in the next 90 digits is 19=10+1+8∗1, then the number of times 1 appears in the next 900 digits is 100+19+19∗8…
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 does tape change on busy beaver look like?
Here is how the changes on the tape look like for the 2-state busy beaver: Tape changes for 2 state busy beaver. Turing Machine for 3-state Busy Beaver: Tape changes for 3 state busy beaver. Turing Machine for 4-state Busy Beaver: Tape changes for 4 state busy beaver.
How big is a busy beaver Turing machine?
Turing Machine for 3-state Busy Beaver: Tape changes for 3 state busy beaver. Turing Machine for 4-state Busy Beaver: Tape changes for 4 state busy beaver. Turing Machine for 5-state Busy Beaver: This image is huge (6146 x 14293 pixels, but only 110KB in size). Click for full size. Tape changes for 5 state busy beaver.