Editing Busy beaver (section)

==Technical definition==
The '''''n''-state busy beaver game''' (or '''BB-''n'' game'''), introduced in [[Tibor Radó]]'s 1962 paper, involves a class of [[Turing machine]]s, each member of which is required to meet the following design specifications:

*The machine has ''n'' "operational" states plus a Halt state, where ''n'' is a positive integer, and one of the ''n'' states is distinguished as the starting state. (Typically, the states are labelled by 1, 2, ..., ''n'', with state 1 as the starting state, or by ''A'', ''B'', ''C'', ..., with state ''A'' as the starting state.)
*The machine uses a single two-way infinite (or unbounded) tape.
*The tape alphabet is {0, 1}, with 0 serving as the blank symbol.
*The machine's ''transition function'' takes two inputs:
:#the current non-Halt state,
:#the symbol in the current tape cell,
:and produces three outputs:
:#a symbol to write over the symbol in the current tape cell (it may be the same symbol as the symbol overwritten),
:#a direction to move (left or right; that is, shift to the tape cell one place to the left or right of the current cell), and
:#a state to transition into (which may be the Halt state).
"Running" the machine consists of starting in the starting state, with the current tape cell being any cell of a blank (all-0) tape, and then iterating the transition function until the Halt state is entered (if ever).  If, and only if, the machine eventually halts, then the number of 1s finally remaining on the tape is called the machine's ''score''. The ''n''-state busy beaver (BB-''n'') game is therefore a contest, depending on definition to find such an ''n''-state Turing machine having the largest possible score or running time.

=== Example ===

The rules for one 1-state Turing machine might be:
* In state 1, if the current symbol is 0, write a 1, move one space to the right, and transition to state 1
* In state 1, if the current symbol is 1, write a 0, move one space to the right, and transition to HALT

This Turing machine would move to the right, swapping the value of all the bits it passes. Since the starting tape is all 0s, it would make an unending string of ones. This machine would not be a busy beaver contender because it runs forever on a blank tape.