Parameterized Verification of Disjunctive Timed Networks
Étienne André, Paul Eichler, Swen Jacobs, Shyam Lal Karra
TL;DR
The paper addresses parameterized verification for disjunctive timed networks (DTNs), where processes synchronize via location guards. It develops an efficient method to compute minimum-time reachability (Minreach) in DTNs using a specialized zone-graph construction on a single TA, avoiding explicit exponential cutoffs. From Minreach, it constructs a summary automaton capturing the local behavior of a single process within any DTN size, enabling verification without building large cutoff systems; it also provides decidability results under certain conditions for invariants and demonstrates practical effectiveness with experiments. Overall, the approach yields a scalable alternative to cutoff-based verification for DTNs and broadens the range of verifiable timing properties in parameterized timed networks.
Abstract
We introduce new techniques for the parameterized verification of disjunctive timed networks (DTNs), i.e., networks of timed automata (TAs) that communicate via location guards that enable a transition only if there is another process in a given location. This computational model has been considered in the literature before, example applications are gossiping clock synchronization protocols or planning problems. We address the minimum-time reachability problem (Minreach) in DTNs, and show how to efficiently solve it based on a novel zone graph algorithm. We further show that solving Minreach allows us to construct a summary TA capturing exactly the possible behaviors of a single TA within a DTN of arbitrary size. The combination of these two results enables the parameterized verification of DTNs, while avoiding the construction of an exponential-size cutoff system required by existing results. Additionally, we develop sufficient conditions for solving Minreach and parameterized verification problems even in certain cases where locations that appear in location guards can have clock invariants, a case that has usually been excluded in the literature. Our techniques are also implemented, and experiments show their practicality.