Reconfigurable Broadcast Networks and Asynchronous Shared-Memory Systems are Equivalent

TL;DR

This paper proves the equivalence of reconfigurable broadcast networks and asynchronous shared-memory systems, showing they can simulate each other and a third model, with implications for analyzing distributed computing systems.

Contribution

It establishes the formal equivalence between RBN and ASMS, enabling transfer of results and insights between these models for distributed computing.

Findings

RBN and ASMS can simulate each other in parameterized reachability.

Both models can simulate IO nets, but not vice versa for a stronger simulation.

Results transfer allows broader analysis of distributed systems.

Abstract

We show the equivalence of two distributed computing models, namely reconfigurable broadcast networks (RBN) and asynchronous shared-memory systems (ASMS), that were introduced independently. Both RBN and ASMS are systems in which a collection of anonymous, finite-state processes run the same protocol. In RBN, the processes communicate by selective broadcast: a process can broadcast a message which is received by all of its neighbors, and the set of neighbors of a process can change arbitrarily over time. In ASMS, the processes communicate by shared memory: a process can either write to or read from a shared register. Our main result is that RBN and ASMS can simulate each other, i.e. they are equivalent with respect to parameterized reachability, where we are given two (possibly infinite) sets of configurations C and C' defined by upper and lower bounds on the number of processes in each state and we would like to decide if some configuration in C can reach some configuration in C'. Using this simulation equivalence, we transfer results of RBN to ASMS and vice versa. Finally, we show that RBN and ASMS can simulate a third distributed model called immediate observation (IO) nets. Moreover, for a slightly stronger notion of simulation (which is satisfied by all the simulations given in this paper), we show that IO nets cannot simulate RBN.