# PRoTECT: Parallelized Construction of Safety Barrier Certificates for Nonlinear Polynomial Systems

arXiv: https://arxiv.org/abs/2404.14804 · HTML: https://mlsanity.com/paper/2404.14804/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2024.

## Built on by (most cited first, 3 of 3)

- [BarrierBench: Evaluating Large Language Models for Safety Verification in Dynamical Systems](https://mlsanity.com/paper/2511.09363/) (2025)
- [k-Inductive Neural Barrier Certificates for Unknown Nonlinear Dynamics](https://mlsanity.com/paper/2605.20108/) (2026)
- [Runtime Monitoring of Supermartingale Certificates](https://mlsanity.com/paper/2610.19701/) (2026)

## Abstract (arXiv)

We develop an open-source software tool, called PRoTECT, for the parallelized construction of safety barrier certificates (BCs) for nonlinear polynomial systems. This tool employs sum-of-squares (SOS) optimization programs to systematically search for polynomial-type BCs, while aiming to verify safety properties over four classes of dynamical systems: (i) discrete-time stochastic systems, (ii) discrete-time deterministic systems, (iii) continuous-time stochastic systems, and (iv) continuous-time deterministic systems. PRoTECT is implemented in Python as an application programming interface (API), offering users the flexibility to interact either through its user-friendly graphic user interface (GUI) or via function calls from other Python programs. PRoTECT leverages parallelism across different barrier degrees to efficiently search for a feasible BC.