578 research outputs found
LazySets.jl: Scalable symbolic-numeric set computations
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.Comment: published in the Proceedings of the JuliaCon Conferences 202
Approximated Symbolic Computations over Hybrid Automata
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the real systems and infinite precision measurements. Such assumptions are not only unrealistic, but often lead to the construction of misleading models. For these reasons we believe that it is necessary to introduce more flexible semantics able to manage with noise, partial information, and finite precision instruments. In particular, in this paper we integrate in a single framework based on approximated semantics different over and under-approximation techniques for hybrid automata. Our framework allows to both compare, mix, and generalize such techniques obtaining different approximated reachability algorithms
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