Paper
StochasticBarrier.jl: A Toolbox for Stochastic Barrier Function Synthesis
Authors
Rayan Mazouz, Frederik Baymler Mathiesen, Luca Laurenti, Morteza Lahijanian
Abstract
We present StochasticBarrier.jl, an open-source Julia-based toolbox for generating Stochastic Barrier Functions (SBFs) for safety verification of discrete-time stochastic systems with additive Gaussian noise. StochasticBarrier.jl certifies linear, polynomial, and piecewise affine (PWA) systems. The latter enables verification for a wide range of system dynamics, including general nonlinear types. The toolbox implements a Sum-of-Squares (SOS) optimization approach, as well as methods based on piecewise constant (PWC) functions. For SOS-based SBFs, StochasticBarrier.jl leverages semi-definite programming solvers, while for PWC SBFs, it offers three engines: two using linear programming (LP) and one based on gradient descent (GD). Benchmarking StochasticBarrier.jl against the state-of-the-art shows that the tool outperforms existing tools in computation time, safety probability bounds, and scalability across over 30 case studies. Compared to its closest competitor, StochasticBarrier.jl is up to four orders of magnitude faster, achieves significant safety probability improvements, and supports higher-dimensional systems.
Metadata
Related papers
Fractal universe and quantum gravity made simple
Fabio Briscese, Gianluca Calcagni • 2026-03-25
POLY-SIM: Polyglot Speaker Identification with Missing Modality Grand Challenge 2026 Evaluation Plan
Marta Moscati, Muhammad Saad Saeed, Marina Zanoni, Mubashir Noman, Rohan Kuma... • 2026-03-25
LensWalk: Agentic Video Understanding by Planning How You See in Videos
Keliang Li, Yansong Li, Hongze Shen, Mengdi Liu, Hong Chang, Shiguang Shan • 2026-03-25
Orientation Reconstruction of Proteins using Coulomb Explosions
Tomas André, Alfredo Bellisario, Nicusor Timneanu, Carl Caleman • 2026-03-25
The role of spatial context and multitask learning in the detection of organic and conventional farming systems based on Sentinel-2 time series
Jan Hemmerling, Marcel Schwieder, Philippe Rufin, Leon-Friedrich Thomas, Mire... • 2026-03-25
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.20359v1</id>\n <title>StochasticBarrier.jl: A Toolbox for Stochastic Barrier Function Synthesis</title>\n <updated>2026-02-23T21:06:30Z</updated>\n <link href='https://arxiv.org/abs/2602.20359v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.20359v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>We present StochasticBarrier.jl, an open-source Julia-based toolbox for generating Stochastic Barrier Functions (SBFs) for safety verification of discrete-time stochastic systems with additive Gaussian noise. StochasticBarrier.jl certifies linear, polynomial, and piecewise affine (PWA) systems. The latter enables verification for a wide range of system dynamics, including general nonlinear types. The toolbox implements a Sum-of-Squares (SOS) optimization approach, as well as methods based on piecewise constant (PWC) functions. For SOS-based SBFs, StochasticBarrier.jl leverages semi-definite programming solvers, while for PWC SBFs, it offers three engines: two using linear programming (LP) and one based on gradient descent (GD). Benchmarking StochasticBarrier.jl against the state-of-the-art shows that the tool outperforms existing tools in computation time, safety probability bounds, and scalability across over 30 case studies. Compared to its closest competitor, StochasticBarrier.jl is up to four orders of magnitude faster, achieves significant safety probability improvements, and supports higher-dimensional systems.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='eess.SY'/>\n <category scheme='http://arxiv.org/schemas/atom' term='math.OC'/>\n <published>2026-02-23T21:06:30Z</published>\n <arxiv:primary_category term='eess.SY'/>\n <author>\n <name>Rayan Mazouz</name>\n </author>\n <author>\n <name>Frederik Baymler Mathiesen</name>\n </author>\n <author>\n <name>Luca Laurenti</name>\n </author>\n <author>\n <name>Morteza Lahijanian</name>\n </author>\n </entry>"
}