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, ������, 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.

Citations