{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-polynomial-stochastic-barrier-functions","title":"On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares","arxiv_id":"2506.09164","date":"2025-06-10","proceeding":null,"authors":["Peter Amorese","Morteza Lahijanian"],"abstract":"Stochastic Barrier Functions (SBFs) certify the safety of stochastic systems by formulating a functional optimization problem, which state-of-the-art methods solve using Sum-of-Squares (SoS) polynomials. This work focuses on polynomial SBFs and introduces a new formulation based on Bernstein polynomials and provides a comparative analysis of its theoretical and empirical performance against SoS methods. We show that the Bernstein formulation leads to a linear program (LP), in contrast to the semi-definite program (SDP) required for SoS, and that its relaxations exhibit favorable theoretical convergence properties. However, our empirical results reveal that the Bernstein approach struggles to match SoS in practical performance, exposing an intriguing gap between theoretical advantages and real-world feasibility.","url_abs":"https://arxiv.org/abs/2506.09164v1","url_pdf":"https://arxiv.org/pdf/2506.09164v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-polynomial-stochastic-barrier-functions","repo_url":"https://github.com/aria-systems-group/berry-er","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}