Automatic Complexity Analysis of Integer Programs via Triangular Weakly Non-Linear Loops

TL;DR

This paper introduces a modular method for analyzing the complexity of integer programs by transforming parts into triangular weakly non-linear loops, enabling bounds computation where other tools fail.

Contribution

It presents a novel modular approach that computes local runtime bounds for subprograms and lifts them to global bounds, implemented in the KoAT tool.

Findings

Successfully analyzes programs where other tools fail

Computes local runtime bounds for subprograms

Lifts local bounds to global program bounds

Abstract

There exist several results on deciding termination and computing runtime bounds for triangular weakly non-linear loops (twn-loops). We show how to use results on such subclasses of programs where complexity bounds are computable within incomplete approaches for complexity analysis of full integer programs. To this end, we present a novel modular approach which computes local runtime bounds for subprograms which can be transformed into twn-loops. These local runtime bounds are then lifted to global runtime bounds for the whole program. The power of our approach is shown by our implementation in the tool KoAT which analyzes complexity of programs where all other state-of-the-art tools fail.