1 research outputs found
A Generic Numbering System based on Catalan Families of Combinatorial Objects
We describe arithmetic algorithms on a canonical number representation based
on the Catalan family of combinatorial objects specified as a Haskell type
class.
Our algorithms work on a {\em generic} representation that we illustrate on
instances members of the Catalan family, like ordered binary and multiway
trees. We validate the correctness of our algorithms by defining an instance of
the same type class based the usual bitstring-based natural numbers.
While their average and worst case complexity is within constant factors of
their traditional counterparts, our algorithms provide super-exponential gains
for numbers corresponding to Catalan objects of low representation size.Comment: preprin