Robust Non-termination Analysis of Numerical Software

TL;DR

This paper presents a method for robustly analyzing nontermination in numerical software, accounting for uncertainties like round-off errors and perturbations, crucial for safety-critical real-time systems.

Contribution

It introduces a novel approach for under-approximating the maximal set of inputs that cause nontermination despite disturbances in numerical programs.

Findings

Effective identification of nontermination inputs under uncertainties

Applicable to safety-critical real-time systems

Validated with multiple illustrative examples

Abstract

Numerical software are widely used in safety-critical systems such as aircrafts, satellites, car engines and so on, facilitating dynamics control of such systems in real time, it is therefore absolutely necessary to verify their correctness. It is a long standing challenge to guarantee verified properties of numerical software are indeed satisfied by their real behaviours, because most of these verifications are conducted under ideal mathematical models, but their real executions could be influenced essentially by uncertain inputs accounting for round-off errors and additive perturbations from real-world phenomena to hardware, which are abstracted away in these ideal mathematical models. In this paper, we attempt to address this issue focusing on nontermination analysis of numerical software, where nontermination is often an unexpected behaviour of computer programs and may be problematic for applications such as real-time systems having hard deadlines on transaction execution time, and propose a method for robust conditional nontermination analysis, which can be used to under-approximate the maximal robust nontermination input set for a given program, from which the program never terminates, regardless of the aforementioned disturbances. Finally, several examples are employed to illustrate our approach.