Chapter

Programming Languages and Systems

Volume 2305 of the series Lecture Notes in Computer Science pp 243-261

Date:

Automatic Complexity Analysis

  • Flemming NielsonAffiliated withInformatics and Mathematical Modelling, The Technical University of Denmark
  • , Hanne Riis NielsonAffiliated withInformatics and Mathematical Modelling, The Technical University of Denmark
  • , Helmut SeidlAffiliated withFachbereich IV — Informatik, Universität Trier

Abstract

We consider the problem of automating the derivation of tight asymptotic complexity bounds for solving Horn clauses. Clearly, the solving time crucially depends on the “sparseness” of the computed relations. Therefore, our asymptotic runtime analysis is accompanied by an asymptotic sparsity calculus together with an asymptotic sparsity analysis. The technical problem here is that least fixpoint iteration fails on asymptotic complexity expressions: the intuitive reason is that O(1)+ srO(1) = O(1) but O(1) + ⋯ + O(1) may return any value.

Keywords

Program analysis Horn clauses automatic complexity analysis sparseness