PURRS: Towards Computer Algebra Support for Fully Automatic Worst-Case Complexity Analysis

TL;DR

This paper introduces PURRS, a system designed to provide comprehensive computer algebra support for fully automatic worst-case complexity analysis, especially handling recurrence relations more effectively.

Contribution

The paper presents PURRS, a new system that enhances computer algebra capabilities to better support automatic worst-case complexity analysis of programs.

Findings

PURRS effectively solves a broader class of recurrence relations.

It reduces the need for user intervention in complexity analysis.

Demonstrated on real-time embedded system programs.

Abstract

Fully automatic worst-case complexity analysis has a number of applications in computer-assisted program manipulation. A classical and powerful approach to complexity analysis consists in formally deriving, from the program syntax, a set of constraints expressing bounds on the resources required by the program, which are then solved, possibly applying safe approximations. In several interesting cases, these constraints take the form of recurrence relations. While techniques for solving recurrences are known and implemented in several computer algebra systems, these do not completely fulfill the needs of fully automatic complexity analysis: they only deal with a somewhat restricted class of recurrence relations, or sometimes require user intervention, or they are restricted to the computation of exact solutions that are often so complex to be unmanageable, and thus useless in practice. In this paper we briefly describe PURRS, a system and software library aimed at providing all the computer algebra services needed by applications performing or exploiting the results of worst-case complexity analyses. The capabilities of the system are illustrated by means of examples derived from the analysis of programs written in a domain-specific functional programming language for real-time embedded systems.