Parametric disjunctive timed networks

TL;DR

This paper studies parametric disjunctive timed networks, showing decidability of certain reachability problems with one clock and no invariants, and highlighting the complexity added by invariants and global properties.

Contribution

It introduces parametric disjunctive timed networks and establishes decidability results for reachability problems with a single clock and no invariants, extending understanding of their computational properties.

Findings

Decidability of local reachability with one clock and no invariants.

Undecidability of global reachability with invariants or multiple parameters.

Decidable subclasses by restricting guard and invariant syntax.

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.