Program transformation by solving recurrences

Abstract

Recursive programs may require large numbers of procedure calls and stack operations, and many such recursive programs exhibit exponential time complexity, due to the time spent re-calculating already computed sub-problems. As a result, methods which transform a given recursive program to an iterative one have been intensively studied. We propose here a new framework for transforming programs by removing recursion. The framework includes a unified method of deriving low time-complexity programs by solving recurrences extracted from the program sources. Our prototype system, APTSR1, is an initial implementation of the framework, automatically finding simpler "closed form" versions of a class of recursive programs. Though in general the solution of recurrences is easier if the functions have only a single recursion parameter, we show a practical technique for solving those with multiple recursion parameters. Copyright © 2006 ACM.