Discrete analogue computing with rotor-routers

TL;DR

This paper explores rotor-router networks as discrete, deterministic analogues of continuous systems and stochastic processes, highlighting their computational capabilities, asynchronous nature, and efficient verifiability.

Contribution

It introduces rotor-router networks as a novel framework for discrete analogue computing, emphasizing their asynchronous, distributed, and verifiable properties.

Findings

Rotor-router networks can perform distributed computations.

They enable efficient verification of computations.

They serve as discrete analogues of linear systems and stochastic processes.

Abstract

Rotor-routing is a procedure for routing tokens through a network that can implement certain kinds of computation. These computations are inherently asynchronous (the order in which tokens are routed makes no difference) and distributed (information is spread throughout the system). It is also possible to efficiently check that a computation has been carried out correctly in less time than the computation itself required, provided one has a certificate that can itself be computed by the rotor-router network. Rotor-router networks can be viewed as both discrete analogues of continuous linear systems and deterministic analogues of stochastic processes.