The placid platypus function, denoted \(\text{PP}(n)\), is an "inverse" of the busy beaver function.[1] [2] \(\text{PP}(n)\) is defined as the minimal number of states needed for a TM that prints a string of \(n\) ones and halts. It was first investigated and named by James Harland[3], as part of his Zany Zoo Turing machine research project[4].
The placid platypus function exhibits much more complex and unpredictable behavior than its inverse. For one, it is non-monotonic. Even its computability is an unsolved problem.
Sources[]
- ↑ James Harland (2016) Busy beaver machines and the observant otter heuristic (or how to tame dreadful dragons) Theoretical Computer Science 646, 20: 61-85. (Preprint at arxiv)
- ↑ James Harland. The Busy Beaver, the Placid Platypus and other Crazy Creatures Twelfth Computing: Australasian Theory Symposium, Hobart (2006) (Archived from the original on 2016-08-20)
- ↑ James Harland at RMIT University, Australia
- ↑ James Harland. The Busy Beaver, the Placid Platypus and other Crazy Creatures