LazySets.jl: Scalable Symbolic-Numeric Set Computations

TL;DR

LazySets.jl is a Julia library that enables scalable, symbolic-numeric set computations, especially for convex and polyhedral sets, facilitating reachability analysis and formal verification in high-dimensional systems.

Contribution

The paper introduces LazySets.jl, a versatile library that combines symbolic and numeric methods for set operations, with efficient algorithms for high-dimensional convex set computations.

Findings

Supports efficient set operations and conversions

Enables high-dimensional reachability analysis

Provides a user-friendly, scalable framework

Abstract

LazySets.jl is a Julia library that provides ways to symbolically represent sets of points as geometric shapes, with a special focus on convex sets and polyhedral approximations. LazySets provides methods to apply common set operations, convert between different set representations, and efficiently compute with sets in high dimensions using specialized algorithms based on the set types. LazySets is the core library of JuliaReach, a cutting-edge software addressing the fundamental problem of reachability analysis: computing the set of states that are reachable by a dynamical system from all initial states and for all admissible inputs and parameters. While the library was originally designed for reachability and formal verification, its scope goes beyond such topics. LazySets is an easy-to-use, general-purpose and scalable library for computations that mix symbolics and numerics. In this article we showcase the basic functionality, highlighting some of the key design choices.