2025/05/24 by Thomas A. Henzinger, Kaushik Mallik, Henzinger, Thomas A. +5 · 5 citations
Computer Science · Decision Sciences · Engineering · #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Electrical engineering #Fault Detection and Control Systems #Logic in Computer Science (cs.LO) #Petri Nets in System Modeling #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2505.18833
openalex publication_date 2025/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present the first supermartingale certificate for quantitative ω-regular properties of discrete-time infinite-state stochastic systems. Our certificate is defined on the product of the stochastic system and a limit-deterministic Büchi automaton that specifies the property of interest; hence we call it a limit-deterministic Büchi supermartingale (LDBSM). Previously known supermartingale certificates applied only to quantitative reachability, safety, or reach-avoid properties, and to qualitative (i.e., probability 1) ω-regular properties. We also present fully automated algorithms for the template-based synthesis of LDBSMs, for the case when the stochastic system dynamics and the controller can be represented in terms of polynomial inequalities. Our experiments demonstrate the ability of our method to solve verification and control tasks for stochastic systems that were beyond the reach of previous supermartingale-based approaches.