Parameterized Verification of Timed Networks with Clock Invariants

TL;DR

The paper addresses parameterized verification for networks of timed automata under three communication primitives: disjunctive guards, lossy broadcast, and k-wise synchronization. It introduces a finite-slot region abstraction to handle clock invariants in DTNs and proves that $PMCP$ over finite local traces is decidable without restriction on invariants. It then shows that lossy broadcast and k-wise synchronized networks can be reduced to DTNs, yielding decidability results and $EXPSPACE$ complexity for location reachability, and extends these results to timed Petri nets. As a milestone, the universal safety problem for timed Petri nets with multiple clocks is decidable, resolving an open question in Abdulla et al. (2018).

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.

Figures (2)

• Figure 1: Asynchronous data read example
• Figure 2: Example of a computation in $\mathit{A}^{3}$ for $\mathit{A}$ as depicted by \ref{['fig:async-read-example']}.

Theorems & Definitions (5)

• Definition 1
• Example 2
• Definition 3: Guarded Timed Automaton (GTA)
• Example 4
• Definition 5: Unguarded Timed Automaton