Parameterized Analysis of Reconfigurable Broadcast Networks (Long Version)

TL;DR

This paper analyzes reconfigurable broadcast networks using a parameterized approach, establishing complexity results for reachability and coverability, and characterizing the computational power of protocols based on RBN.

Contribution

It introduces a parameterized analysis framework for RBN, proves PSPACE-completeness results, and characterizes the predicates computable by RBN protocols.

Findings

Reachability from a cube to another cube is PSPACE-complete.

Almost-sure coverability problem is PSPACE-complete for RBN.

Characterization of predicates computable by RBN protocols.

Abstract

Reconfigurable broadcast networks (RBN) are a model of distributed computation in which agents can broadcast messages to other agents using some underlying communication topology which can change arbitrarily over the course of executions. In this paper, we conduct parameterized analysis of RBN. We consider cubes,(infinite) sets of configurations in the form of lower and upper bounds on the number of agents in each state, and we show that we can evaluate boolean combinations over cubes and reachability sets of cubes in PSPACE. In particular, reachability from a cube to another cube is a PSPACE-complete problem. To prove the upper bound for this parameterized analysis, we prove some structural properties about the reachability sets and the symbolic graph abstraction of RBN, which might be of independent interest. We justify this claim by providing two applications of these results. First, we show that the almost-sure coverability problem is PSPACE-complete for RBN, thereby closing a complexity gap from a previous paper. Second, we define a computation model using RBN, \`a la population protocols, called RBN protocols. We characterize precisely the set of predicates that can be computed by such protocols.