Generalizations
For any model of computation there exist simple analogs of the busy beaver. For example, the generalization to Turing machines with n states and m symbols defines the following generalized busy beaver functions:
- Σ(n, m): the largest number of non-zeros printable by an n-state, m-symbol machine started on an initially blank tape before halting, and
- S(n, m): the largest number of steps taken by an n-state, m-symbol machine started on an initially blank tape before halting.
For example the longest running 3-state 3-symbol machine found so far runs 119,112,334,170,342,540 steps before halting. The longest running 6-state, 2-symbol machine which has the additional property of reversing the tape value at each step produces 6,147 1s after 47,339,970 steps. So SRTM(6) ≥ 47,339,970 and ΣRTM(6) ≥ 6,147.
Likewise we could define an analog to the Σ function for register machines as the largest number which can be present in any register on halting, for a given number of instructions.
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