Reachability analysis of linear hybrid systems via block decomposition

Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous and discrete post operators to compute states reachable according to continuous and discrete dynamics, respectively. In this paper, we enhance both of these operators and make sure that most of the involved computations are performed in low-dimensional state space. In particular, we improve the continuous-post operator by performing computations in high-dimensional state space only for time intervals relevant for the subsequent application of the discrete-post operator. Furthermore, the new discrete-post operator performs low-dimensional computations by leveraging the structure of the guard and assignment of a considered transition. We illustrate the potential of our approach on a number of challenging benchmarks.Comment: Accepted at EMSOFT 202

ARCH-COMP19 Category Report: Continuous and hybrid systems with nonlinear dynamics

We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2019. In this year, 6 tools Ariadne, CORA, DynIbex, Flow*, Isabelle/HOL, and JuliaReach (in alphabetic order) participated. They are applied to solve reachability analysis problems on four benchmark problems, one of them with hybrid dynamics. We do not rank the tools based on the results, but show the current status and discover the potential advantages of different tools

Decomposed Reachability Analysis for Nonlinear Systems

We introduce an approach to conservatively abstract a nonlinear continuous system by a hybrid automaton whose continuous dynamics are given by a decomposition of the original dynamics. The decomposed dynamics is in the form of a set of lower-dimensional ODEs with time-varying uncertainties whose ranges are defined by the hybridization domains. We propose several techniques in the paper to effectively compute abstractions and flowpipe overapproximations. First, a novel method is given to reduce the overestimation accumulation in a Taylor model flowpipe construction scheme. Then we present our decomposition method, as well as the framework of on-the-fly hybridization. A combination of the two techniques allows us to handle much larger, nonlinear systems with comparatively large initial sets. Our prototype implementation is compared with existing reachability tools for offline and online flowpipe construction on challenging benchmarks of dimensions ranging from 7 to 30. Our code has successfully passed the artifact evaluatio