Zippy Tabulations of Recursive Functions

Abstract

This paper is devoted to the statement and proof of a theorem showing how recursive definitions whose associated call graphs satisfy certain shape conditions can be converted systematically into efficient bottom-up tabulation schemes. The increase in efficiency can be dramatic, typically transforming an exponential time algorithm into one that takes only quadratic time. The proof of the theorem relies heavily on the theory of zips developed by Roland Backhouse and Paul Hoogendijk.