The placid platypus function, denoted \(\text{PP}(n)\), is an "inverse" of the busy beaver function.[1] \(\text{PP}(n)\) 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, as part of his "Zany Zoo" Turing machine research project.

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 Edit