Effective Stochastic Automata Model Checking by Interval Abstraction (extended version)

2026-07-01

AI Summary

Existing approaches struggle to perform efficient and general-purpose model checking for stochastic automata with arbitrary probability distributions, particularly due to limitations in handling nondeterminism and complex probabilistic dependencies. This work proposes a novel method that integrates refinable interval abstraction with a “large-step” semantics, enabling—for the first time—the computation of sound upper and lower bounds on reachability probabilities for general stochastic automata. The approach extends the Modest and Jani modeling languages and is implemented in a prototype tool built in Rust. Experimental results demonstrate that the method effectively handles non-trivial instances under minimal input restrictions, delivering reliable probability bounds and overcoming prior limitations that restricted applicability to narrow subclasses or lacked scalability.

Abstract

Stochastic automata (SA) are a formal stochastic continuous-time model based on countdown timers whose expiration times follow general probability distributions. SA are particularly useful to faithfully model and analyse dependable systems involving faults, maintenance, and repairs. Effective SA analysis approaches have so far been limited to statistical model checking and thus deterministic SA, while previously proposed model-checking techniques apply to limited subclasses of SA only, or do not scale. In this paper, we present the first dedicated SA model checking approach that is general and effective: It puts few restrictions on the input SA, and we show in our experimental evaluation that it works well for nontrivial examples. It combines a refinable interval abstraction of the continuous distributions with a direct application of the "big time steps" semantics of SA, providing upper/lower bounds on maximum/minimum reachability probabilities. We extend the Modest and Jani modelling formalisms with support for SA, and provide a prototype implementation of our approach in Rust.

Problem

• Stochastic Automata
• Model Checking
• Continuous-Time Systems
• Reachability Probabilities
• General Distributions

Innovation

• stochastic automata
• interval abstraction
• model checking
• reachability probabilities
• continuous-time systems