Reconfiguration and Message Losses in Parameterized Broadcast Networks

TL;DR

This paper establishes tight bounds on the minimal number of nodes and execution length for coverability in reconfigurable broadcast networks, introduces a model with message losses, and analyzes their computational complexity.

Contribution

It provides the first tight bounds for cutoff and execution length in reconfigurable networks and extends analysis to lossy networks with static topology.

Findings

Cutoff is linear in the number of protocol states.

Execution length is quadratic in the number of protocol states.

Lossy networks can have shorter executions than reconfigurable networks.

Abstract

Broadcast networks allow one to model networks of identical nodes communicating through message broadcasts. Their parameterized verification aims at proving a property holds for any number of nodes, under any communication topology, and on all possible executions. We focus on the coverability problem which dually asks whether there exists an execution that visits a configuration exhibiting some given state of the broadcast protocol. Coverability is known to be undecidable for static networks, i.e. when the number of nodes and communication topology is fixed along executions. In contrast, it is decidable in PTIME when the communication topology may change arbitrarily along executions, that is for reconfigurable networks. Surprisingly, no lower nor upper bounds on the minimal number of nodes, or the minimal length of covering execution in reconfigurable networks, appear in the literature. In this paper we show tight bounds for cutoff and length, which happen to be linear and quadratic, respectively, in the number of states of the protocol. We also introduce an intermediary model with static communication topology and non-deterministic message losses upon sending. We show that the same tight bounds apply to lossy networks, although, reconfigurable executions may be linearly more succinct than lossy executions. Finally, we show NP-completeness for the natural optimisation problem associated with the cutoff.