# JuliaReach: a Toolbox for Set-Based Reachability

## TL;DR

JuliaReach is a versatile toolbox for set-based reachability analysis of dynamical systems, combining lazy and explicit set computations in Julia for efficient, large-scale problem solving.

## Contribution

It introduces a new Julia toolbox with both reachability algorithms and convex set calculus, enabling efficient analysis of complex systems.

## Key findings

- Achieves runtime performance comparable to compiled languages.
- Handles high-dimensional lazy set operations efficiently.
- Applicable to large-scale, complex dynamical systems.

## Abstract

We present JuliaReach, a toolbox for set-based reachability analysis of dynamical systems. JuliaReach consists of two main packages: Reachability, containing implementations of reachability algorithms for continuous and hybrid systems, and LazySets, a standalone library that implements state-of-the-art algorithms for calculus with convex sets. The library offers both concrete and lazy set representations, where the latter stands for the ability to delay set computations until they are needed. The choice of the programming language Julia and the accompanying documentation of our toolbox allow researchers to easily translate set-based algorithms from mathematics to software in a platform-independent way, while achieving runtime performance that is comparable to statically compiled languages. Combining lazy operations in high dimensions and explicit computations in low dimensions, JuliaReach can be applied to solve complex, large-scale problems.