State-Space Abstractions for Parametric Timed Games

2026-06-19

AI Summary

This work addresses the state-space explosion problem in parameterized timed games under temporal uncertainty and adversarial environments by proposing a general state abstraction framework. It systematically extends techniques such as double inclusion, zone merging, convex hull computation, and location abstraction to parameterized timed games for the first time, while rigorously preserving the correctness of parameter synthesis and winning strategies. Built upon parameterized timed automata, game semantics, and formal verification methods, the framework substantially enhances scalability and successfully solves previously intractable instances on both established manufacturing cell benchmarks and novel adversarial Internet-of-Things scenarios.

Abstract

Synthesizing controllers for real-time systems under both timing uncertainty and adversarial environments requires exploring prohibitively large symbolic state spaces. While zone inclusion checking has been applied to Parametric Timed Games, more aggressive abstractions from the Parametric Timed Automata and Timed Games literature -- double inclusion, zone merging, hull abstractions, and location-based abstraction -- have not yet been lifted to the parametric game setting. We define a general abstraction framework for Parametric Timed Games, instantiate it with each of the aforementioned abstractions, and prove that the framework preserves correctness of parameter synthesis and winning strategies. Experimental results on an established production cell benchmark and a novel adversarial IoT case study show that the abstractions significantly improve scalability, solving instances previously intractable for existing techniques.

Problem

• Parametric Timed Games
• State-Space Abstraction
• Controller Synthesis
• Real-Time Systems
• Adversarial Environment

Innovation

• Parametric Timed Games
• State-Space Abstraction
• Zone Inclusion
• Controller Synthesis
• Scalability