Keyword Analysis & Research: busy beaver 5


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How many 1s does a busy beaver machine produce?

The current (as of 2018) 5-state busy beaver champion produces 4098 1s, using 47 176 870 steps (discovered by Heiner Marxen and Jürgen Buntrock in 1989), but there remain 18 or 19 (possibly under 10, see below) machines with non-regular behavior which are believed to never halt, but which have not been proven to run infinitely.

What is the busy beaver 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. The rules for the 2-state game are as follows:

What is a busy beaver 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.

How many states do you need for the busy beaver function?

It is extremely hard to prove values for the busy beaver function (and the max shift function). It has only been proven for extremely small machines with fewer than five states, while one would presumably need at least 20-50 states to make a useful machine.


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