Parameterized Verification of Timed Networks with Clock Invariants

2024-08-09

arXiv.org

AI Summary

This paper addresses the model-checking problem for parameterized networks of timed automata with clock invariants, supporting disjunctive guards, lossy broadcast, and k-synchronization communication mechanisms. To resolve the open problem—posed by Abdulla et al. (2018)—of general safety decidability for multi-clock timed Petri nets, we propose a compositional verification framework integrating timed automata modeling, disjunctive location guards, parameterized abstraction, and antichain techniques. We establish, for the first time under general assumptions, the decidability of both local trace properties and global configuration reachability for parameterized timed networks with clock invariants—including those featuring disjunctions or lossy broadcast. Furthermore, we reveal an essential verification equivalence between disjunctive timed networks and lossy broadcast networks. Our results provide the first theoretical foundation for parameterized verification of large-scale real-time distributed systems incorporating clock invariants.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Distributed Problem Solving

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

We consider parameterized verification problems for networks of timed automata (TAs) that communicate via disjunctive guards or lossy broadcast. To this end, we first consider disjunctive timed networks (DTNs), i.e., networks of TAs that communicate via location guards that enable a transition only if there is another process in a certain location. We solve for the first time the general case with clock invariants, and establish the decidability of the parameterized verification problem for local trace properties and for reachability of global configurations; Moreover, we prove that, surprisingly and unlike in other settings, this model is equivalent to lossy broadcast networks.

Problem

• Verifying timed networks with unrestricted clock invariants
• Reducing parameterized verification to single automaton analysis
• Solving decidability of universal safety for timed Petri nets

Innovation

• Parameterized verification with unrestricted clock invariants
• Reduction of PMCP to single timed automaton
• Solving decidability for timed Petri nets