# busy beaver

(classic problem)

**Definition:**
(1) A *Turing machine* with a small number of *states* that halts when started with a blank tape, but writes a huge number of non-blanks or takes a huge number of steps. (2) The problem of finding the maximum number of non-blanks written or steps taken for any Turing machines with a given number of states and symbols.

*Note:
The problem is well-defined but rapidly becomes impractical to determine for even a small number of states and symbols. This problem is related to the **halting problem* since one must determine if a machine is looping or eventually halts.

Author: PEB

## More information

History, explanation, and links about the Busy Beaver Turing Machine. Heiner Marxen's currently known busy beaver results page.

Go to the
Dictionary of Algorithms and Data
Structures home page.

If you have suggestions, corrections, or comments, please get in touch
with Paul Black.

Entry modified 2 November 2007.

HTML page formatted Mon Feb 2 13:10:39 2015.

Cite this as:

Paul E. Black, "busy beaver", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 2 November 2007. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/busyBeaver.html