BB(1,m): Difference between revisions
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(Created page with "{| class="wikitable" |+ Small busy beaver values<ref>P. Michel, "[https://bbchallenge.org/~pascal.michel/ha.html Historical survey of Busy Beavers]".</ref> ! !!1-state |- ! 2-symbol | BB(1) = 1 (Halt) |}") |
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BB(1,m) is the Busy Beaver problem for 1-state, m-symbol TMs. They are relatively trivial. No matter how many symbols you have, [[TNF]] only has access to a single transition, the initial <code>A0</code> transition. In fact, there are only 3 different turing machines in [[TNF]]: One halting: <code>A0:1RZ</code> and 2 trivial [[Translated Cyclers]]: <code>A0:0RA</code> and <code>A0:1RA</code>. These are effectively 1-instruction TMs in [[BBi]]. As a result S(1,m) = 1 and Σ(1,m) = 1. | |||
==Champions== | |||
|- | S(1,m) = 1, achieved by: | ||
* {{TM|1RZ---|halt}} | |||
Σ(1,m) = 1, achieved by: | |||
|} | * {{TM|1RZ---|halt}} | ||
[[Category:BB Domains]] | |||
Latest revision as of 20:40, 25 August 2025
BB(1,m) is the Busy Beaver problem for 1-state, m-symbol TMs. They are relatively trivial. No matter how many symbols you have, TNF only has access to a single transition, the initial A0 transition. In fact, there are only 3 different turing machines in TNF: One halting: A0:1RZ and 2 trivial Translated Cyclers: A0:0RA and A0:1RA. These are effectively 1-instruction TMs in BBi. As a result S(1,m) = 1 and Σ(1,m) = 1.
Champions
S(1,m) = 1, achieved by:
1RZ---(bbch)
Σ(1,m) = 1, achieved by:
1RZ---(bbch)