Formalising and monitoring traffic rules for autonomous vehicles in Isabelle/HOL

A Rizaldi, J Keinholz, M Huber, J Feldle… - … Formal Methods: 13th …, 2017 - Springer
Recent accidents involving autonomous vehicles prompt us to consider how we can
engineer an autonomous vehicle which always obeys traffic rules. This is particularly …

Methods for order reduction of zonotopes

AK Kopetzki, B Schürmann… - 2017 IEEE 56th Annual …, 2017 - ieeexplore.ieee.org
Zonotopes are a special subclass of polytopes, which have several favorable properties:
They can be represented in a compact way and they are closed under the Minkowski sum as …

Verified reachability analysis of continuous systems

F Immler - Tools and Algorithms for the Construction and Analysis …, 2015 - Springer
Ordinary differential equations (ODEs) are often used to model the dynamics of (often safety-
critical) continuous systems. This work presents the formal verification of an algorithm for …

A formally verified motion planner for autonomous vehicles

A Rizaldi, F Immler, B Schürmann, M Althoff - International Symposium on …, 2018 - Springer
Autonomous vehicles are safety-critical cyber-physical systems. To ensure their correctness,
we use a proof assistant to prove safety properties deductively. This paper presents a …

On computing the minkowski difference of zonotopes

M Althoff - arXiv preprint arXiv:1512.02794, 2015 - arxiv.org
Zonotopes are becoming an increasingly popular set representation for formal verification
techniques. This is mainly due to their efficient representation and their favorable …

A verified ODE solver and the Lorenz attractor

F Immler - Journal of automated reasoning, 2018 - Springer
A rigorous numerical algorithm, formally verified with Isabelle/HOL, is used to certify the
computations that Tucker used to prove chaos for the Lorenz attractor. The verification is …

The flow of ODEs: Formalization of variational equation and Poincaré map

F Immler, C Traut - Journal of Automated Reasoning, 2019 - Springer
Formal analysis of ordinary differential equations (ODEs) and dynamical systems requires a
solid formalization of the underlying theory. The formalization needs to be at the correct level …

A verified certificate checker for finite-precision error bounds in Coq and HOL4

H Becker, N Zyuzin, R Monat… - … Formal Methods in …, 2018 - ieeexplore.ieee.org
Being able to soundly estimate roundoff errors of finite-precision computations is important
for many applications in embedded systems and scientific computing. Due to the …

The flow of ODEs

F Immler, C Traut - … Theorem Proving: 7th International Conference, ITP …, 2016 - Springer
Formal analysis of ordinary differential equations (ODEs) and dynamical systems requires a
solid formalization of the underlying theory. The formalization needs to be at the correct level …

Time-triggered conversion of guards for reachability analysis of hybrid automata

S Bak, S Bogomolov, M Althoff - Formal Modeling and Analysis of Timed …, 2017 - Springer
A promising technique for the formal verification of embedded and cyber-physical systems is
flow-pipe construction, which creates a sequence of regions covering all reachable states …