Placid Platypus: Difference between revisions
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Loader3229 (talk | contribs) Created page with "The '''Placid Platypus''' function <math>PP(n)</math> <ref>James Harland. [https://dl.acm.org/doi/pdf/10.5555/1151785.1151794 The Busy Beaver, the Placid Platypus and other Crazy Creatures]. 2006.</ref> is the minimal number of states of 2-symbol Turing machines that print exactly n ones when halt. <math> PP(n) \leq n </math>, because you can print each 1 in a state. Also if <math> n > \Sigma(m)</math>, then <math> PP(n) > m </math>. == References == <references /> ..." |
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<math> PP(n) \leq n </math>, because you can print each 1 in a state. Also if <math> n > \Sigma(m)</math>, then <math> PP(n) > m </math>. | <math> PP(n) \leq n </math>, because you can print each 1 in a state. Also if <math> n > \Sigma(m)</math>, then <math> PP(n) > m </math>. | ||
== Values == | |||
{| class="wikitable" | |||
!n | |||
!<math>PP(n)</math> | |||
!TM | |||
|- | |||
|1 | |||
|1 | |||
|{{TM|1RZ---|halt}} | |||
|- | |||
|2 | |||
|2 | |||
|{{TM|1RB---_1RZ---|halt}} | |||
|- | |||
|3 | |||
|2 | |||
|{{TM|1RB1LA_1LA1RZ|halt}} | |||
|- | |||
|4 | |||
|2 | |||
|{{TM|1RB1LB_1LA1RZ|halt}} | |||
|} | |||
== References == | == References == | ||
<references /> | <references /> | ||
[[Category:Functions]] | [[Category:Functions]] | ||
Revision as of 15:17, 28 September 2026
The Placid Platypus function [1] is the minimal number of states of 2-symbol Turing machines that print exactly n ones when halt.
, because you can print each 1 in a state. Also if , then .
Values
| n | TM | |
|---|---|---|
| 1 | 1 | 1RZ--- (bbch)
|
| 2 | 2 | 1RB---_1RZ--- (bbch)
|
| 3 | 2 | 1RB1LA_1LA1RZ (bbch)
|
| 4 | 2 | 1RB1LB_1LA1RZ (bbch)
|
References
- ↑ James Harland. The Busy Beaver, the Placid Platypus and other Crazy Creatures. 2006.