Parametric disjunctive timed networks
Étienne André, Swen Jacobs, Engel Lefaucheux
TL;DR
The paper studies parametrised verification of distributed real-time systems modeled as networks of parametric timed processes connected by location guards. It introduces parametric disjunctive timed networks (PDTNs) and analyzes the parametrised reachability-emptiness problem for local and global properties, showing decisive results: local reachability is decidable for 1-clock PDTNs without invariants (arbitrary timing parameters), while invariants or global properties drive undecidability; and it identifies decidable subclasses such as fully parametric PDTNs with a single parameter and L/U-parametric PDTNs. These findings delineate the boundaries of decidability in guarded, multi-process timed networks and highlight the strong impact of invariants on expressiveness. The work contributes to the theory of parametric real-time verification and informs the design of scalable verification techniques for distributed systems with timing uncertainties.
Abstract
We consider distributed systems with an arbitrary number of processes, modelled by timed automata that communicate through location guards: a process can take a guarded transition if at least one other process is in a given location. In this work, we introduce parametric disjunctive timed networks, where each timed automaton may contain timing parameters, i.e. unknown constants. We investigate two problems: deciding the emptiness of the set of parameter valuations for which 1) a given location is reachable for at least one process (local property), and 2) a global state is reachable where all processes are in a given location (global property). Our main positive result is that the first problem is decidable for networks of processes with a single clock and without invariants; this result holds for arbitrarily many timing parameters -- a setting with few known decidability results. However, it becomes undecidable when invariants are allowed, or when considering global properties, even for systems with a single parameter. This highlights the significant expressive power of invariants in these networks. Additionally, we exhibit further decidable subclasses by restraining the syntax of guards and invariants.