BB(1,m): Difference between revisions
Jump to navigation
Jump to search
(→Champions: Made champions section consistent with other domain pages) |
(Added note about Σ(1,1)) |
||
| Line 1: | Line 1: | ||
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. | 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. Note that Σ(1,1) = 0 as 1-symbol TMs cannot print non-zero symbols. | ||
==Champions== | ==Champions== | ||
Latest revision as of 15:54, 30 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. Note that Σ(1,1) = 0 as 1-symbol TMs cannot print non-zero symbols.
Champions
S(1,m) = 1 and Σ(1,m) = 1 are both achieved by only one champion in TNF:
1RZ---(bbch)