# ARCH-COMP18 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics

by Matthias Althoff, Stanley Bak, Xin Chen, Chuchu Fan, Marcelo Forets, Goran Frehse, Niklas Kochdumper, Yangge Li, Sayan Mitra, Rajarshi Ray, Christian Schilling and Stefan Schupp (2018)

## Publication

ARCH-COMP18 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics. Matthias Althoff, Stanley Bak, Xin Chen, Chuchu Fan, Marcelo Forets, Goran Frehse, Niklas Kochdumper, Yangge Li, Sayan Mitra, Rajarshi Ray, Christian Schilling and Stefan Schupp (2018) ARCH18. 5th International Workshop on Applied Verification of Continuous and Hybrid Systems, 54: 23–52. doi: 10.29007/73mb.

## Abstract

This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with linear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2018. In its second edition, 9 tools have been applied to solve six different benchmark problems in the category for linear continuous dynamics (in alphabetical order): CORA, CORA/SX, C2E2, Flow*, HyDRA, Hylaa, Hylaa-Continuous, JuliaReach, SpaceEx, and XSpeed. This report is a snapshot of the current landscape of tools and the types of benchmarks they are particularly suited for. Due to the diversity of problems, we are not ranking tools, yet the presented results probably provide the most complete assessment of tools for the safety verification of continuous and hybrid systems with linear continuous dynamics up to this date.

## Contributions

This report summarizes results obtained in the 2018 friendly competition of the ARCH workshop for verifying hybrid systems with linear continuous dynamics $$\dot{x}(t) = Ax(t) + Bu(t),$$ where $A \in \mathbb{R}^{n \times n}$, $x \in \mathbb{R}^n$, $B \in \mathbb{R}^{n \times m}$, and $u \in \mathbb{R}^m$. Participating tools are summarized in Sec. 2. The results of our selected benchmark problems are shown in Sec. 3 and are obtained on the tool developers’ own machines. Thus, one has to factor in the computational power of the processors used, summarized in Appendix A, as well as the efficiency of the programming language of the tools. The goal of the friendly competition is not to rank the results, but rather to present the landscape of existing solutions in a breadth that is not possible with scientific publications in classical venues. Such publications would typically require the presentation of novel techniques, while this report showcases the current state-of-the-art tools. For all results reported by each participant, we have run an independent repeatability evaluation. The selection of the benchmarks has been conducted within the forum of the ARCH website (cps-vo.org/group/ARCH), which is visible for registered users and registration is open for anybody. All tools presented in this report use some form of reachability analysis. This, however, is not a constraint set by the organizers of the friendly competition. We hope to encourage further tool developers to showcase their results in future editions.

## How to cite

@inproceedings{ARCH18:ARCH_COMP18_Category_Report_Continuous,
author    = {Matthias Althoff and Stanley Bak and Xin Chen and Chuchu Fan and Marcelo Forets and Goran Frehse and Niklas Kochdumper and Yangge Li and Sayan Mitra and Rajarshi Ray and Christian Schilling and Stefan Schupp},
title     = {ARCH-COMP18 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics},
booktitle = {ARCH18. 5th International Workshop on Applied Verification of Continuous and Hybrid Systems},
editor    = {Goran Frehse},
series    = {EPiC Series in Computing},
volume    = {54},
pages     = {23--52},
year      = {2018},
publisher = {EasyChair},
bibsource = {EasyChair, https://easychair.org},
issn      = {2398-7340},
url       = {https://easychair.org/publications/paper/4cGr},
doi       = {10.29007/73mb}}

##### Marcelo Forets
###### Universidad de la República, Uruguay

My research includes developing numerical methods and software that impact decisions regarding reliability, correctness and safety of systems. I specialize on formal verification of Cyber-Physical Systems (CPS), hybrid dynamical systems, and robustness analysis of neural networks.