arXiv subjects

Luko van der Maas

Publications and source records attributed to Luko van der Maas.

3 recordsLinked to original sources

arXiv2026

Fast Computation of Conditional Probabilities in MDPs and Markov Chain Families

Computing optimal conditional reachability probabilities in Markov decision processes (MDPs) is tractable by a reduction to reachability probabilities. Yet, this reduction yields cyclic, challenging MDPs that are often notoriously hard to solve. We present an alternative, practically efficient method to compute optimal conditional reachabilities. This new method is numerically stable, can decide the threshold problem in linear time on acyclic MDPs, and yields performance comparable to standard reachability queries. We also integrate the method in an abstraction-refinement framework to analyse millions of Markov chains at once. We demonstrate the efficacy of the new methods on benchmarks from Bayesian network analysis, probabilistic programs, and runtime monitoring and show speed-ups up to multiple orders of magnitude.

cs.LO↗

arXiv2026

Learning Robust Markov Models for Safe Runtime Monitoring

We present a model-based approach to learning robust runtime monitors for autonomous systems. Runtime monitors play a crucial role in raising the level of assurance by observing system behavior and predicting potential safety violations. In our approach, we propose to capture a system's (stochastic) behavior using interval Hidden Markov Models (iHMMs). The monitor then uses this learned iHMM to derive risk estimates for potential safety violations. The paper makes three key contributions: (1) it provides a formalization of the problem of learning robust runtime monitors, (2) introduces a novel framework that uses conformance-testing-based refinement for learning robust iHMMs with convergence guarantees, and (3) presents an efficient monitoring algorithm for computing risk estimates over iHMMs. Our empirical results demonstrate the efficacy of monitors learned using our approach, particularly when compared to model-free monitoring approaches that rely solely on collected data without access to a system model.

cs.LO↗

arXiv2025

Learning Verified Monitors for Hidden Markov Models

Runtime monitors assess whether a system is in an unsafe state based on a stream of observations. We study the problem where the system is subject to probabilistic uncertainty and described by a hidden Markov model. A stream of observations is then unsafe if the probability of being in an unsafe state is above a threshold. A correct monitor recognizes the set of unsafe observations. The key contribution of this paper is the first correct-by-construction synthesis method for such monitors, represented as finite automata. The contribution combines four ingredients: First, we establish the coNP-hardness of checking whether an automaton is a correct monitor, i.e., a monitor without misclassifications. Second, we provide a reduction that reformulates the search for misclassifications into a standard probabilistic system synthesis problem. Third, we integrate the verification routine into an active automata learning routine to synthesize correct monitors. Fourth, we provide a prototypical implementation that shows the feasibility and limitations of the approach on a series of benchmarks.

cs.FL↗