Parameterized verification of synchronization in constrained reconfigurable broadcast networks

TL;DR

This paper studies how constraints on reconfiguration affect the decidability and complexity of verifying synchronization in reconfigurable broadcast networks, showing that certain bounds lead to undecidability while others remain tractable.

Contribution

It introduces a detailed analysis of the impact of reconfiguration constraints on the parameterized verification of synchronization, identifying conditions for decidability and complexity.

Findings

Synchronization is decidable in PTIME when reconfiguration bounds grow with the number of agents.

Bounding reconfigured links by a constant makes the synchronization problem undecidable.

The complexity of synchronization verification depends critically on the nature of reconfiguration constraints.

Abstract

Reconfigurable broadcast networks provide a convenient formalism for modelling and reasoning about networks of mobile agents broadcasting messages to other agents following some (evolving) communication topology. The parameterized verification of such models aims at checking whether a given property holds irrespective of the initial configuration (number of agents, initial states and initial communication topology). We focus here on the synchronization property, asking whether all agents converge to a set of target states after some execution. This problem is known to be decidable in polynomial time when no constraints are imposed on the evolution of the communication topology (while it is undecidable for static broadcast networks). In this paper we investigate how various constraints on reconfigurations affect the decidability and complexity of the synchronization problem. In particular, we show that when bounding the number of reconfigured links between two communications steps by a constant, synchronization becomes undecidable; on the other hand, synchronization remains decidable in PTIME when the bound grows with the number of agents.