arXiv subjects

Gabriel Dengler

Publications and source records attributed to Gabriel Dengler.

4 recordsLinked to original sources

arXiv2026

A Taxonomy of Distance Metrics for Time-Sensitive Importance Splitting: Timer Bounds, Resampling, and the Global Age

Importance splitting (ISPLIT) evaluates the probabilities of rare events in non-Markovian models. It requires a heuristic importance function (IFUN) that estimates the distance to the target. While including timer evaluations in the IFUN can substantially improve the effectiveness of ISPLIT, the existing time-sensitive IFUNs evaluate simulation states with respect to single sampled timer values. Thus, reaching highly important states requires simultaneously sampling specific combinations of timer values, yielding several unproductive simulation runs. In this paper, we revisit time-sensitive ISPLIT with the goal of steering simulation runs towards important states. First, we study how timer values can be resampled conditioned on the elapsed time. The importance can be evaluated by considering the set of feasible timer values, decoupling importance estimation from timer samples. Second, we exploit the global age of a simulation to identify and prune the executions that can no longer reach the target within the remaining time budget. Together, these ideas lead to a taxonomy of distance metrics clarifying the role of timer bounds, resampling, and the global age. In particular, for models with unbounded timers, we show that time-sensitive IFUNs collapse to ordinary IFUNs under resampling. Experiments demonstrate that the proposed formulations substantially improve the accuracy of ISPLIT estimators.

stat.ME↗

arXiv2025

Automata Learning -- Expect Delays!

This paper studies active automata learning (AAL) in the presence of stochastic delays. We consider Mealy machines that have stochastic delays associated with each transition and explore how the learner can efficiently arrive at faithful estimates of those machines, the precision of which crucially relies on repetitive sampling of transition delays. While it is possible to na\"ively integrate the delay sampling into AAL algorithms such as $L^*$, this leads to considerable oversampling near the root of the state space. We address this problem by separating conceptually the learning of behavior and delays such that the learner uses the information gained while learning the logical behavior to arrive at efficient input sequences for collecting the needed delay samples. We put emphasis on treating cases in which identical input/output behaviors might stem from distinct delay characteristics. Finally, we provide empirical evidence that our method outperforms the na\"ive baseline across a wide range of benchmarks and investigate its applicability in a realistic setting by studying the join order in a relational database.

cs.FL↗

arXiv2025

Time-Sensitive Importance Splitting

State-of-the-art methods for rare event simulation of non-Markovian models face practical or theoretical limits if observing the event of interest requires prior knowledge or information on the timed behavior of the system. In this paper, we attack both limits by extending importance splitting with a time-sensitive importance function. To this end, we perform backwards reachability search from the target states, considering information about the lower and upper bounds of the active timers in order to steer the generation of paths towards the rare event. We have developed a prototype implementation of the approach for input/output stochastic automata within the Modest Toolset. Preliminary experiments show the potential of the approach in estimating rare event probabilities for an example from reliability engineering.

cs.LO↗

arXiv2024

Transient Evaluation of Non-Markovian Models by Stochastic State Classes and Simulation

Non-Markovian models have great expressive power, at the cost of complex analysis of the stochastic process. The method of Stochastic State Classes (SSCs) derives closed-form analytical expressions for the joint Probability Density Functions (PDFs) of the active timers with marginal expolynomial PDF, though being hindered by the number of concurrent non-exponential timers and of discrete events between regenerations. Simulation is an alternative capable of handling the large class of PDFs samplable via inverse transform, which however suffers from rare events. We combine these approaches to analyze time-bounded transient properties of non-Markovian models. We enumerate SSCs near the root of the state-space tree and then rely on simulation to reach the target, affording transient evaluation of models for which the method of SSCs is not viable while reducing computational time and variance of the estimator of transient probabilities with respect to simulation. Promising results are observed in the estimation of rare event probabilities.

cs.LO↗