Parameterized Verification of Timed Networks with Clock Invariants

TL;DR

This paper advances parameterized verification for networks of timed automata by solving the model checking problem with unrestricted clock invariants and reducing complex communication primitives to simpler DTN cases, enabling decidability results.

Contribution

It introduces methods to reduce parameterized model checking problems for various timed automata networks to simpler cases, solving open problems in the field.

Findings

PMCP over finite local traces reduces to single TA model checking.

PMCP for lossy broadcast networks reduces to DTNs.

Location reachability in k-wise synchronized networks reduces to DTNs.

Abstract

We consider parameterized verification problems for networks of timed automata (TAs) based on different communication primitives. 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 case with unrestricted clock invariants, and establish that the parameterized model checking problem (PMCP) over finite local traces can be reduced to the corresponding model checking problem on a single TA. Moreover, we prove that the PMCP for networks that communicate via lossy broadcast can be reduced to the PMCP for DTNs. Finally, we show that for networks with k-wise synchronization, and therefore also for timed Petri nets, location reachability can be reduced to location reachability in DTNs. As a consequence we can answer positively the open problem from Abdulla et al.(2018) whether the universal safety problem for timed Petri nets with multiple clocks is decidable.