ARCH-COMP17 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics

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 2017. In its first edition, seven tools have been applied to solve three different benchmark problems in the category for linear continuous dynamics (in alphabetical order): Axelerator, CORA, Flow*, HyDRA, Hylaa, SpaceEx, and XSpeed. The result 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.

Reachability Analysis of Large Linear Systems With Uncertain Inputs in the Krylov Subspace

“…PSfrag replacements c g (1) g (2) g (3) c ⊕ g (1) c ⊕ g (1) ⊕ g (2) c ⊕ g (1) ⊕ g (2) ⊕ g (3) construction direction "⊕" "⊕" Figure 1.…”

“…At the time the approach in [37] was proposed, tools for reachability analysis had an exponential complexity as well, so that overall the computation time could be significantly reduced. However, modern tools such as SpaceEx [29], Flow* [18], HyLAA [15], XSpeed [36], or CORA [2] have a polynomial complexity, as demonstrated in [3], and thus would most certainly outperform the technique proposed in [37], even without any order reduction. The same authors later combined reachability analysis with Krylov subspace approximation methods [38].…”

ARCH-COMP19 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics

“…For the 2019 edition, we have decided to keep all benchmarks from our 2018 friendly competition [2], but solve them with our updated tools. In addition, we have modified the Spacecraft Rendezvous benchmark and the Gearbox benchmark.…”

“…• Building benchmark from [27,No. 2]: A purely continuous linear system with a medium number of continuous state variables; the benchmark does not only have safety properties, but also ones that should be violated to check whether the reachable sets contain certain states.…”

Numerical Verification of 10000-dimensional Linear Systems 10000x Faster

“…In particular, when using support functions to encode only the linear constraints used in the safety property, a highly-efficient method results. This approach was used by SpaceEx in the piece-wise affine reachability competition in ARCH17 for the building benchmark, where a single support function direction allowed the analysis to quickly complete [3]. Although having a small output space makes the linear map operation efficient, like zonotopes, the full matrix exponential must still be computed.…”