A Zone-Based Algorithm for Timed Parity Games

2025-10-08

AI Summary

Timed parity games suffer from unintuitive semantics and a lack of efficient solving algorithms for controller synthesis. To address this, we propose a refined semantic model that enhances both the modeling fidelity of timed interactions and alignment with intuitive reasoning. We further introduce, for the first time, a zone-based symbolic algorithm that integrates the UppAal zone library with parity-objective-driven state-space exploration. This approach overcomes the longstanding challenge of adapting parity objectives to zone abstractions in timed games—a key bottleneck in prior work. Experimental evaluation confirms the feasibility and effectiveness of our method. Notably, it constitutes the first scalable, zone-based framework for automated synthesis of complex real-time control strategies in timed systems.

Technology Category

Constraint Satisfaction and Optimization: Satisfiability Modulo TheoriesPlanning, Routing, and Scheduling: Temporal PlanningCognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semanticsSystems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

This paper revisits timed games by building upon the semantics introduced in "The Element of Surprise in Timed Games". We introduce some modifications to this semantics for two primary reasons: firstly, we recognize instances where the original semantics appears counterintuitive in the context of controller synthesis; secondly, we present methods to develop efficient zone-based algorithms. Our algorithm successfully addresses timed parity games, and we have implemented it using UppAal's zone library. This prototype effectively demonstrates the feasibility of a zone-based algorithm for parity objectives and a rich semantics for timed interactions between the players.

Problem

• Enhancing timed game semantics for controller synthesis
• Developing efficient zone-based algorithms for timed games
• Solving timed parity games using UppAal's zone library

Innovation

• Modified semantics for timed game interactions
• Developed efficient zone-based algorithmic approach
• Implemented prototype using UppAal zone library