Stateless Computation

TL;DR

This paper introduces a model of stateless distributed computation inspired by Internet routing, analyzing its self-stabilization conditions and computational capabilities, especially on ring topologies, revealing significant power with logarithmic message labels.

Contribution

It provides a comprehensive analysis of the conditions for self-stabilization and demonstrates the computational power of stateless protocols, including a separation between unidirectional and bidirectional rings.

Findings

Logarithmic-length labels enable substantial computational power.

Necessary conditions and hardness results for self-stabilization are established.

A separation between unidirectional and bidirectional rings in computational complexity.

Abstract

We present and explore a model of stateless and self-stabilizing distributed computation, inspired by real-world applications such as routing on today's Internet. Processors in our model do not have an internal state, but rather interact by repeatedly mapping incoming messages ("labels") to outgoing messages and output values. While seemingly too restrictive to be of interest, stateless computation encompasses both classical game-theoretic notions of strategic interaction and a broad range of practical applications (e.g., Internet protocols, circuits, diffusion of technologies in social networks). We embark on a holistic exploration of stateless computation. We tackle two important questions: (1) Under what conditions is self-stabilization, i.e., guaranteed "convergence" to a "legitimate" global configuration, achievable for stateless computation? and (2) What is the computational power of stateless computation? Our results for self-stabilization include a general necessary condition for self-stabilization and hardness results for verifying that a stateless protocol is self-stabilizing. Our main results for the power of stateless computation show that labels of logarithmic length in the number of processors yield substantial computational power even on ring topologies. We present a separation between unidirectional and bidirectional rings (L/poly vs. P/poly), reflecting the sequential nature of computation on a unidirectional ring, as opposed to the parallelism afforded by the bidirectional ring. We leave the reader with many exciting directions for future research.