Papers › Abstraction-based Synthesis for Stochastic Systems with Omega-Regular Objectives
Abstraction-based Synthesis for Stochastic Systems with Omega-Regular Objectives
Maxence Dutreix, Jeongmin Huh, Samuel Coogan
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
This paper studies the synthesis of controllers for discrete-time, continuous state stochastic systems subject to omega-regular specifications using finite-state abstractions. We present a synthesis algorithm for minimizing or maximizing the probability that a discrete-time stochastic system with finite number of modes satisfies an omega-regular property. Our approach uses a finite-state abstraction of the underlying dynamics in the form of a Bounded-parameter Markov Decision Process (BMDP) arising from a finite partition of the system's domain. Such abstractions allow for a range of transition probabilities between states for each action. Our method analyzes the product between the abstraction and a Deterministic Rabin Automaton encoding the specification. Synthesis is decomposed into a qualitative problem, where the greatest permanent winning components of the product are created, and a quantitative problem, which requires maximizing the probability of reaching this component. We propose a metric for the quality of the controller with respect to the abstracted states and devise a domain partition refinement technique to reach a quality target. Next, we present a method for computing controllers for stochastic systems with a continuous input set. The system is assumed to be affine in input and disturbance, and we derive a technique for solving the qualitative and quantitative problems in the abstractions of such systems called Controlled Interval-valued Markov Chains. The greatest permanent component of such abstractions are found by partitioning the input space to generate a BMDP accounting for all possible qualitative transitions between states. Maximizing the probability of reaching this component is cast as an optimization problem. Quality of the synthesized controller and a refinement scheme are described for this framework.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections