Reconfigurable Broadcast Networks (RBN) are a model for large groups of identical agents communicating via unreliable broadcast. A pushdown RBN (PRBN) is simply one where each agent is modeled by a pushdown transition system. A PRBN on a message alphabet \(\mathcal{M}\) is described by a pushdown automaton \(\mathcal{A}\) over the alphabet \( \{br(m), rec(m) | m \in \mathcal{M} \}\). Configurations of \(\mathcal{A}\), i.e., pairs \((q, \sigma)\) of state and stack content, are called local configurations.\(\\ \)

A configuration of the PRBN is a function from a finite set of agents \(\mathbb{A}\) to local configurations. A run starts with an arbitrarily large set of agents, all in the initial state with an empty stack . A step consists of one agent taking a transition with a broadcast \(br(m)\), and each other agent either not moving or taking a transition \(rec(m)\) (in other words, one agent broadcasts and other agents non-deterministically receive the broadcast or not).\(\\ \)