online statistical model checking

This work addresses the challenge of verifying Markov decision processes (MDPs) with unknown transition probabilities that exhibit both nondeterminism and probabilistic uncertainty. To tackle this problem, the authors propose an online statistical model checking method grounded in confidence sequences. By integrating dynamic sampling, statistical hypothesis testing, and a novel online confidence sequence construction, the approach effectively mitigates the conservativeness and inefficiency inherent in traditional union-bound techniques. The resulting specialized verification tool maintains rigorous reliability guarantees while achieving a dramatic reduction in sample complexity—requiring on average approximately 50 times fewer samples than the current state-of-the-art methods—thereby substantially enhancing both efficiency and practical applicability.

For Markov decision processes (MDPs) with unknown transition probabilities, existing statistical model checking (SMC) algorithms suffer from high sample complexity and weak theoretical guarantees. Method: We introduce tight concentration inequalities—specifically, the Bretagnolle–Huber and Empirical Bernstein bounds—into the SMC framework for the first time, and design adaptive, structure-aware statistical estimators that exploit MDP topology. Contribution/Results: Theoretically, our approach yields significantly tighter and more general probably approximately correct (PAC) guarantees. Empirically, it reduces required sample sizes by up to two orders of magnitude on standard verification benchmarks. This work establishes a new paradigm for efficient and reliable formal verification of uncertain systems.

Statistical Model Checking (SMC) often yields inflated error rates in probabilistic and expected reward estimation due to insufficient statistical rigor. To address this, we propose a robust estimation framework with rigorous theoretical guarantees: (i) we extend the Dvoretzky–Kiefer–Wolfowitz (DKW) inequality to expected reward estimation for the first time; (ii) we introduce a limit-PAC (Probably Approximately Correct) procedure ensuring controllable estimation error; and (iii) we derive a computable upper bound on reachability rewards and enhance practicality via path truncation and distribution bounding. Our method is implemented in the *modes* tool. Experimental evaluation demonstrates a substantial reduction in erroneous conclusions while maintaining high precision, thereby ensuring both statistical correctness and engineering applicability.

This paper presents a systematic survey of probabilistic model checking (PMC) over the past 25 years, addressing the longstanding challenges of reliability verification for complex stochastic systems and the limited industrial adoption of formal methods. It analyzes PMC’s evolving applications across communication protocols, bio-computing, and artificial intelligence, and traces core technical advances rooted in Markov chains, probabilistic temporal logics (PTL), and efficient symbolic algorithms. The paper introduces an innovative “application–theory–tool” tri-dimensional evolutionary framework, revealing how domain-driven requirements shape methodological adaptation. It consolidates representative success stories to empirically demonstrate PMC’s indispensable role in ensuring safety and reliability. Finally, it identifies three key future directions: heterogeneous stochastic modeling, scalable verification, and human-in-the-loop verification—aimed at extending formal methods to industrial-scale, real-world stochastic systems.

Traditional model confidence sets rely on the fixed-sample assumption, rendering them inadequate for continuous model selection and uncertainty quantification under dynamic data streams. To address this, we introduce the first sequential extension of model confidence sets, proposing a dynamic model screening framework grounded in e-processes, confidence sequences, and sequential hypothesis testing. Our method requires no prespecified stopping rule and delivers, at any time, a nonasymptotic, time-uniform confidence set that provably covers the true optimal model subset with guaranteed nominal coverage probability. Unlike static approaches, it substantially enhances statistical robustness and real-time adaptability in online model evaluation. The framework provides both theoretical guarantees and practical tools for trustworthy model selection in streaming data analysis.

该研究探讨了加权模型计数和概率模型检测之间的关系，通过映射方法将两者联系起来，并讨论了如何跨框架转移优化技术。

该研究使用概率模型检测方法解决自回归神经序列模型在部署时的约束违反概率和输入满足领域需求比例的问题。

This study addresses the lack of rigorous statistical guarantees in sequential sampling for auditing by formulating it as a sequential hypothesis test under sampling without replacement from a finite population. It defines null and alternative hypotheses based on a tolerable deviation rate and constructs exact stopping and decision rules that provide a priori control over both Type I and Type II error probabilities. The work introduces the first sequential audit sampling framework supporting one-sided, two-stage, and truncated designs. Exact boundaries are derived using finite-population error probabilities and efficiently calibrated via Monte Carlo simulation under the least favorable deviation rate. This approach not only ensures pre-specified error control but also accurately estimates expected sample sizes, making it suitable for attribute sampling and tests of controls.

This study addresses the computational redundancy and prohibitive simulation costs arising from the independent verification of composite scenarios in safety-critical domains such as autonomous driving. To this end, this work proposes a scenario-based compositional statistical model checking framework. It introduces a pioneering scenario-level compositional verification paradigm that decomposes composite scenarios and safety specifications into atomic units, verifies them independently, and subsequently composes the estimated results. By integrating importance sampling, kernel density estimation, and parallelization strategies, the framework eliminates redundant computations through structural reuse. Furthermore, it enables low-cost, rapid querying for previously unseen composite scenarios. Experimental results demonstrate that the proposed approach significantly reduces simulation overhead while maintaining high accuracy, thereby substantially enhancing overall verification efficiency.

为解决概率模型检测中的状态空间爆炸问题，提出了一种基于规范指导的路径缩短方法，特别针对马尔可夫链和ω-正则属性，以提高验证效率。