Phase-Bounded Broadcast Networks over Topologies of Communication

TL;DR

This paper investigates the decidability of coverability in broadcast networks with bounded phases of broadcasting and receiving, showing complexity results for different bounds and topologies.

Contribution

It introduces a phase-bounded approximation of the coverability problem, establishing decidability and complexity results for various bounds and topologies.

Findings

Decidability for k=2, EXPSPACE-complete for k=1

Undecidability persists for k>6

Polynomial-time solution for line topologies at k=1 and k=2

Abstract

We study networks of processes that all execute the same finite state protocol and that communicate through broadcasts. The processes are organized in a graph (a topology) and only the neighbors of a process in this graph can receive its broadcasts. The coverability problem asks, given a protocol and a state of the protocol, whether there is a topology for the processes such that one of them (at least) reaches the given state. This problem is undecidable. We study here an under-approximation of the problem where processes alternate a bounded number of times $k$ between phases of broadcasting and phases of receiving messages. We show that, if the problem remains undecidable when $k$ is greater than 6, it becomes decidable for $k=2$, and EXPSPACE-complete for $k=1$. Furthermore, we show that if we restrict ourselves to line topologies, the problem is in $P$ for $k=1$ and $k=2$.