On-The-Fly Symbolic Algorithm for Timed ATL with Abstractions

2025-06-09

AI Summary

Verifying Timed Alternating-Time Temporal Logic (TATL) specifications for multi-component real-time systems under distributed control is notoriously challenging due to state-space explosion and bottlenecks in dynamic dependency graph reduction. This paper proposes a novel dynamic symbolic verification algorithm built upon an Abstract Dependency Graph (ADG) framework. It introduces, for the first time, an inclusion-free abstraction mechanism that overcomes classical ADG limitations on formula expressiveness, enabling on-demand exploration of the full TATL state space. The approach integrates game-theoretic semantic modeling with symbolic model checking and is deeply embedded into an extended version of the Uppaal platform. Experimental evaluation demonstrates that our method achieves nearly 100× speedup over naïve enumeration, significantly outperforms Uppaal Tiga—which supports only a fragment of TATL—and improves overall Uppaal performance by approximately 10× when integrated.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Planning, Routing, and Scheduling: Temporal Planning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Verification of real-time systems with multiple components controlled by multiple parties is a challenging task due to its computational complexity. We present an on-the-fly algorithm for verifying timed alternating-time temporal logic (TATL), a branching-time logic with quantifiers over outcomes that results from coalitions of players in such systems. We combine existing work on games and timed CTL verification in the abstract dependency graph (ADG) framework, which allows for easy creation of on-the-fly algorithms that only explore the state space as needed. In addition, we generalize the conventional inclusion check to the ADG framework which enables dynamic reductions of the dependency graph. Using the insights from the generalization, we present a novel abstraction that eliminates the need for inclusion checking altogether in our domain. We implement our algorithms in Uppaal and our experiments show that while inclusion checking considerably enhances performance, our abstraction provides even more significant improvements, almost two orders of magnitude faster than the naive method. In addition, we outperform Uppaal Tiga, which can verify only a strict subset of TATL. After implementing our new abstraction in Uppaal Tiga, we also improve its performance by almost an order of magnitude.

Problem

• Verifying real-time multi-component systems controlled by multiple parties
• Developing on-the-fly algorithm for timed alternating-time temporal logic (TATL)
• Enhancing performance via dynamic abstraction and inclusion checks

Innovation

• On-the-fly algorithm for TATL verification
• Dynamic reduction via abstract dependency graphs
• Novel abstraction eliminating inclusion checking