Placid Platypus - Revision history

Sligocki: Good point about the Sigma vs S issue, sigh. This also makes it unclear to me if it is computable. I think the S version would be, but not the Sigma version.

2026-09-28T17:02:54Z

Good point about the Sigma vs S issue, sigh. This also makes it unclear to me if it is computable. I think the S version would be, but not the Sigma version.

← Older revision		Revision as of 17:02, 28 September 2026
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	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.		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>. On the other side, there is also a connection to [[Lazy Beaver]] (~~or, a variant that is instead~~ determined by ones rather than steps): if <math>n < LB(m)</math> then <math>PP(n) \le 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>. On the other side, there is also a connection to a variation of the [[Lazy Beaver]] function (determined by ones rather than steps): if <math>n < LB_\Sigma(m)</math> then <math>PP(n) \le m</math>.

	Note that this function is not strictly increasing, and that it is computable.		Note that this function is not strictly increasing, and that it may be computable.

	== Values ==		== Values ==

HelpMe: elaboration

2026-09-28T16:53:32Z

elaboration

@@ Line 1: / Line 1: @@
 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>. On the other side, there is also a connection to [[Lazy Beaver]]: if <math>n < LB(m)</math> then <math>PP(n) \le 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>. On the other side, there is also a connection to [[Lazy Beaver]] (or, a variant that is instead determined by ones rather than steps): if <math>n < LB(m)</math> then <math>PP(n) \le m</math>.
 == Values ==
@@ Line 7: / Line 9: @@
 !n
 !<math>PP(n)</math>
-!TM
+!Example TM
 |-
 |1
@@ Line 24: / Line 26: @@
 |2
 |{{TM|1RB1LB_1LA1RZ|halt}}
 |}
 == References ==
 <references />
 [[Category:Functions]]

Sligocki: Comment about LB connection.

2026-09-28T16:08:12Z

Comment about LB connection.

← Older revision		Revision as of 16:08, 28 September 2026
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	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.		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>.		<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>. On the other side, there is also a connection to [[Lazy Beaver]]: if <math>n < LB(m)</math> then <math>PP(n) \le m</math>.

	== Values ==		== Values ==

Loader3229 at 15:17, 28 September 2026

2026-09-28T15:17:59Z

@@ 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>.
+== Values ==
 == References ==
 <references />
 [[Category:Functions]]

Loader3229: Created page with "The '''Placid Platypus''' function $PP(n)$ James Harland. [https://dl.acm.org/doi/pdf/10.5555/1151785.1151794 The Busy Beaver, the Placid Platypus and other Crazy Creatures]. 2006. is the minimal number of states of 2-symbol Turing machines that print exactly n ones when halt. $PP(n) \leq n$ , because you can print each 1 in a state. Also if $n > \Sigma(m)$ , then $PP(n) > m$ . == References == ..."

2026-09-28T15:16:08Z

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 /> ..."

New page

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 />
[[Category:Functions]]