Placid Platypus: Difference between revisions

From BusyBeaverWiki
Jump to navigation Jump to search
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 /> ..."
 
No edit summary
Line 3: Line 3:
<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 PP(n) [1] is the minimal number of states of 2-symbol Turing machines that print exactly n ones when halt.

PP(n)≤n, because you can print each 1 in a state. Also if n>Σ(m), then PP(n)>m.

Values

n PP(n) TM
1 1 1RZ--- (bbch)
2 2 1RB---_1RZ--- (bbch)
3 2 1RB1LA_1LA1RZ (bbch)
4 2 1RB1LB_1LA1RZ (bbch)

References